This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Ber...This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.展开更多
The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and...The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.展开更多
Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx 4 and V(x)=(1/2)x 2+λx 2α with α=2,3,4 and doubly anharmonic os...Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx 4 and V(x)=(1/2)x 2+λx 2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x 2+λ 1x 4 +λ 2x 6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.展开更多
For toe-shooting method, geomaterial constitutive models concerned are studied. Analysis shows that, although extensively applied in soil mechanics, due to its angular singularity of yielding surface, the Mohr-Coulomb...For toe-shooting method, geomaterial constitutive models concerned are studied. Analysis shows that, although extensively applied in soil mechanics, due to its angular singularity of yielding surface, the Mohr-Coulomb model is not suitable for numerical simulations in large deformation; in this case the rock-fills may be regarded as the Drucker-Prager model and the seaooze as the Prandtl-Reuss model. By comparing experimental data with numerical results, the constitutive model of the seaooze is numerically verified. It shows that, in high strain rate stage forming the blasting crater, the seaooze behaves as ideal non-compressible fluid, while in low strain rate stage during which the reck-fills flow to the blasting crater, the viscosity of the seaooze is negligible.展开更多
Sulfuric acid-phenol and sulfuric acid-anthrone methods were used to detect polysaccharide content in shoots of Aralia elata（ Miq.） Seem.,and the conversion factor to glucose was measured with refined polysaccharide...Sulfuric acid-phenol and sulfuric acid-anthrone methods were used to detect polysaccharide content in shoots of Aralia elata（ Miq.） Seem.,and the conversion factor to glucose was measured with refined polysaccharides. Comprehensive evaluation was carried out by linear relationship,precision,reproducibility,stability and recovery rate. The results showed that the linear relationship between glucose concentration and absorbance was good when glucose concentration was0-40 μg/ml,and the average recovery rate was equal to or higher than 97. 00% with good reproducibility（ RSD 〈 1. 60%,n = 5）. It revealed that the two methods were accurate and reliable,and suitable for the determination of polysaccharide content in the shoots of A. elata. Polysaccharide content detected by sulfuric acid-phenol and sulfuric acid-anthrone methods was 19. 31% and 20. 40% respectively.展开更多
Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point b...Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity.展开更多
This study explores the 2D stretching flow of a hybrid nanofluid over a curved surface influenced by a magnetic field and reactions. A steady laminar flow model is created with curvilinear coordinates, considering the...This study explores the 2D stretching flow of a hybrid nanofluid over a curved surface influenced by a magnetic field and reactions. A steady laminar flow model is created with curvilinear coordinates, considering thermal radiation, suction, and magnetic boundary conditions. The nanofluid is made of water with copper and MWCNTs as nanoparticles. The equations are transformed into nonlinear ODEs and solved numerically. The model’s accuracy is confirmed by comparing it with published data. Results show that fluid velocity increases, temperature decreases, and concentration increases with the curvature radius parameter. The hybrid nanofluid is more sensitive to magnetic field changes in velocity, while the nanofluid is more sensitive to magnetic boundary coefficient changes. These insights can optimize heat and mass transfer in industrial processes like chemical reactors and wastewater treatment.展开更多
文摘This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.
文摘The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.
文摘Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx 4 and V(x)=(1/2)x 2+λx 2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x 2+λ 1x 4 +λ 2x 6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.
基金Sponsored by the National Natural Science Foundation of China (10072070)
文摘For toe-shooting method, geomaterial constitutive models concerned are studied. Analysis shows that, although extensively applied in soil mechanics, due to its angular singularity of yielding surface, the Mohr-Coulomb model is not suitable for numerical simulations in large deformation; in this case the rock-fills may be regarded as the Drucker-Prager model and the seaooze as the Prandtl-Reuss model. By comparing experimental data with numerical results, the constitutive model of the seaooze is numerically verified. It shows that, in high strain rate stage forming the blasting crater, the seaooze behaves as ideal non-compressible fluid, while in low strain rate stage during which the reck-fills flow to the blasting crater, the viscosity of the seaooze is negligible.
基金Supported by Scientific Research Project of Education Department of Liaoning Province,China(L2017lkyfwdf-05)Public Welfare Fund Project of Department of Science and Technology of Liaoning Province,China(2016003003)
文摘Sulfuric acid-phenol and sulfuric acid-anthrone methods were used to detect polysaccharide content in shoots of Aralia elata（ Miq.） Seem.,and the conversion factor to glucose was measured with refined polysaccharides. Comprehensive evaluation was carried out by linear relationship,precision,reproducibility,stability and recovery rate. The results showed that the linear relationship between glucose concentration and absorbance was good when glucose concentration was0-40 μg/ml,and the average recovery rate was equal to or higher than 97. 00% with good reproducibility（ RSD 〈 1. 60%,n = 5）. It revealed that the two methods were accurate and reliable,and suitable for the determination of polysaccharide content in the shoots of A. elata. Polysaccharide content detected by sulfuric acid-phenol and sulfuric acid-anthrone methods was 19. 31% and 20. 40% respectively.
文摘Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity.
文摘This study explores the 2D stretching flow of a hybrid nanofluid over a curved surface influenced by a magnetic field and reactions. A steady laminar flow model is created with curvilinear coordinates, considering thermal radiation, suction, and magnetic boundary conditions. The nanofluid is made of water with copper and MWCNTs as nanoparticles. The equations are transformed into nonlinear ODEs and solved numerically. The model’s accuracy is confirmed by comparing it with published data. Results show that fluid velocity increases, temperature decreases, and concentration increases with the curvature radius parameter. The hybrid nanofluid is more sensitive to magnetic field changes in velocity, while the nanofluid is more sensitive to magnetic boundary coefficient changes. These insights can optimize heat and mass transfer in industrial processes like chemical reactors and wastewater treatment.
