Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge t...Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.展开更多
Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to sol...Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.展开更多
This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,w...This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.展开更多
In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Kl...In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.展开更多
Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement trans...Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.展开更多
In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contou...In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the Stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.展开更多
With the advancement of technology,exploring the impact of digital transformation on vocational education English teaching has become crucial.This study aims to investigate the effectiveness of digital transformation ...With the advancement of technology,exploring the impact of digital transformation on vocational education English teaching has become crucial.This study aims to investigate the effectiveness of digital transformation in English teaching in vocational education in China by exploring students’and teachers’attitudes,views,and experiences on the use of digital technology in English teaching.This study employed a mixed method of qualitative and quantitative analysis.The research results indicate that digital transformation has had a positive impact on vocational education English teaching,as it enhances the teaching process,promotes communication and collaboration,and increases students’enthusiasm and participation.However,implementing digital transformation in vocational education English teaching also poses challenges,including a lack of resources,infrastructure,and training.This study provides an in-depth understanding of the advantages and challenges of digital transformation in vocational education English teaching and proposes strategies to improve the implementation of digital technology in this context.展开更多
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t...We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.展开更多
This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence ...This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations (PDEs) are transformed into a system of coupled non-linear ordinary differential equations (ODEs) with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method (DTM). The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.展开更多
In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to ana...In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.展开更多
Previous studies have proposed higher requirements for the transient characteristics of a DC transformer used in a flexible high-voltage direct current(HVDC) system to achieve faster sampling speed and meet wider band...Previous studies have proposed higher requirements for the transient characteristics of a DC transformer used in a flexible high-voltage direct current(HVDC) system to achieve faster sampling speed and meet wider bandwidth requirements of the control and protection signal, and to eventually suppress the large transient fault current. In this study, a transient characteristics verification method is proposed for transient characteristics verification of a DC transformer used in a flexible HVDC system based on resampling technology and LabVIEW measurement technology after analyzing the key technology for transient characteristics verification of a DC transformer. A laboratory experiment for the transient characteristics of a full-fiber electronic DC transformer is conducted, and experimental results show that such verification method can be employed for frequency response and step response verification of a DC transformer at 10% of the rated voltage and current, and can eventually improve the screening of a DC transformer.展开更多
In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solution...In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.展开更多
Orthorhombic LiMnO2 cathode materials were synthesized successfully at lower temperature by sol-gel method. When LiMnO2 precursor prepared by sol-gel method was fired in air, the product was a mixture of spinel struct...Orthorhombic LiMnO2 cathode materials were synthesized successfully at lower temperature by sol-gel method. When LiMnO2 precursor prepared by sol-gel method was fired in air, the product was a mixture of spinel structure LiMn2O4 and rock-salt structure Li2MnO3, whereas in argon single-phase orthorhombic LiMnO2 could obtain at the range of 750℃ to 920℃. The substitution of Mn by Zn2+ or Co3+ in LiMnO2 led to the structure of LiMnO2 transiting to Qα-LiFeO2. The results of electrochemical cycles indicated that the discharged capacity of orthorhombic-LiMnO2 was smaller at the initial stages, then gradually increased with the increasing of cycle number, finally the capacity stabilized to certain value after about 10th cycles. This phenomenon reveals that there is an activation process for orthorhombic LiMnO2 cathode materials during electrochemical cycles, which is a phase transition process from orthorhombic LiMnO2 to tetragonal spinel Li2Mn2O4. The capacity of orthorhombic LiMnO2 synthesized at lower temperature is larger than that synthesized at high temperature.展开更多
In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.
In this paper, the genera]ised two-dimensiona] differentia] transform method (DTM) of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method (DTM) of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12326305,11931017,and 12271490)the Excellent Youth Science Fund Project of Henan Province(Grant No.242300421158)+2 种基金the Natural Science Foundation of Henan Province(Grant No.232300420119)the Excellent Science and Technology Innovation Talent Support Program of ZUT(Grant No.K2023YXRC06)Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。
文摘Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
文摘Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.
基金funded by the Deanship of Research in Zarqa University,Jordan。
文摘This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.
文摘In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.
基金supported financially by the National Natural Science Foundation of China (NSFC) (Grant No.51775378)the Key Projects in Tianjin Science&Technology Support Program (Grant No.19YFZC GX00890).
文摘Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.
文摘In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the Stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.
基金Hainan Vocational University of Science and Technology Educational Reform Project“Research on Digital Transformation in Vocational Education English Teaching”(HKJG2024-01)。
文摘With the advancement of technology,exploring the impact of digital transformation on vocational education English teaching has become crucial.This study aims to investigate the effectiveness of digital transformation in English teaching in vocational education in China by exploring students’and teachers’attitudes,views,and experiences on the use of digital technology in English teaching.This study employed a mixed method of qualitative and quantitative analysis.The research results indicate that digital transformation has had a positive impact on vocational education English teaching,as it enhances the teaching process,promotes communication and collaboration,and increases students’enthusiasm and participation.However,implementing digital transformation in vocational education English teaching also poses challenges,including a lack of resources,infrastructure,and training.This study provides an in-depth understanding of the advantages and challenges of digital transformation in vocational education English teaching and proposes strategies to improve the implementation of digital technology in this context.
文摘We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.
文摘This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations (PDEs) are transformed into a system of coupled non-linear ordinary differential equations (ODEs) with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method (DTM). The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.
基金The project partly supported by the Foundation of Zhongshan University Advanced Research Center
文摘In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.
基金supported by the State Grid Corporation Science and Technology Project(No.JL71-15-039)
文摘Previous studies have proposed higher requirements for the transient characteristics of a DC transformer used in a flexible high-voltage direct current(HVDC) system to achieve faster sampling speed and meet wider bandwidth requirements of the control and protection signal, and to eventually suppress the large transient fault current. In this study, a transient characteristics verification method is proposed for transient characteristics verification of a DC transformer used in a flexible HVDC system based on resampling technology and LabVIEW measurement technology after analyzing the key technology for transient characteristics verification of a DC transformer. A laboratory experiment for the transient characteristics of a full-fiber electronic DC transformer is conducted, and experimental results show that such verification method can be employed for frequency response and step response verification of a DC transformer at 10% of the rated voltage and current, and can eventually improve the screening of a DC transformer.
文摘In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.
基金supported by the National Natural Science Foundation of China under grant No.59972026.
文摘Orthorhombic LiMnO2 cathode materials were synthesized successfully at lower temperature by sol-gel method. When LiMnO2 precursor prepared by sol-gel method was fired in air, the product was a mixture of spinel structure LiMn2O4 and rock-salt structure Li2MnO3, whereas in argon single-phase orthorhombic LiMnO2 could obtain at the range of 750℃ to 920℃. The substitution of Mn by Zn2+ or Co3+ in LiMnO2 led to the structure of LiMnO2 transiting to Qα-LiFeO2. The results of electrochemical cycles indicated that the discharged capacity of orthorhombic-LiMnO2 was smaller at the initial stages, then gradually increased with the increasing of cycle number, finally the capacity stabilized to certain value after about 10th cycles. This phenomenon reveals that there is an activation process for orthorhombic LiMnO2 cathode materials during electrochemical cycles, which is a phase transition process from orthorhombic LiMnO2 to tetragonal spinel Li2Mn2O4. The capacity of orthorhombic LiMnO2 synthesized at lower temperature is larger than that synthesized at high temperature.
文摘In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method (DTM) of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.