Anovel accuratemethod is proposed to solve a broad variety of linear and nonlinear(1+1)-dimensional and(2+1)-dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic ...Anovel accuratemethod is proposed to solve a broad variety of linear and nonlinear(1+1)-dimensional and(2+1)-dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity.For(1+1)-dimensional problems,analytical solutions that satisfy the boundary requirements are derived.Such solutions are numerically calculated using the trigonometric basis approximation for(2+1)-dimensional problems.With the aid of these analytical or numerical approximations,the original problems can be converted into the fractional ordinary differential equations,and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients.An efficient backward substitution strategy that was previously provided for a single fractional ordinary differential equation is then used to solve the corresponding systems.The straightforward quasilinearization technique is applied to handle nonlinear issues.Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.展开更多
The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling...The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling effects of embedded pipes plays an essential role in the design of the structure and its cooling system. In this study, the singular boundary method, a semi-analytical meshless technique, was employed to analyze the temperature distribution. A numerical algorithm solved the transient temperature field with consideration of the effects of cooling pipe specification, isolation of heat of hydration, and ambient temperature. Numerical results are verified through comparison with those of the finite element method, demonstrating that the proposed approach is accurate in the simulation of the thermal field in concrete structures with a water cooling pipe.展开更多
In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can si...In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can significantly reduce the difficulty in the inverse wave source recovery problem,only needing to solve a few equations in the problem domain,since the initial condition/boundary conditions and a supplementary final time condition are satisfied automatically.As a consequence,the eigenfunctions are used to expand the trial solutions,and then a small scale linear system is solved to determine the expansion coefficients from the differencing equations.Because the ill-posedness of the inverse wave source problem is greatly reduced,the present method is accurate and stable against a large noise up to 50%,of which the numerical tests confirm the observation.展开更多
Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equa...Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures.By introducing the velocity resonance mechanism to the multiple kink solutions,we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients.The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited.After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada-Kotera-Caudrey-Dodd-Gibbons(SKCDG)equation,the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.展开更多
基金the National Key Research and Development Program of China(No.2021YFB2600704)the National Natural Science Foundation of China(No.52171272)the Significant Science and Technology Project of the Ministry of Water Resources of China(No.SKS-2022112).
文摘Anovel accuratemethod is proposed to solve a broad variety of linear and nonlinear(1+1)-dimensional and(2+1)-dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity.For(1+1)-dimensional problems,analytical solutions that satisfy the boundary requirements are derived.Such solutions are numerically calculated using the trigonometric basis approximation for(2+1)-dimensional problems.With the aid of these analytical or numerical approximations,the original problems can be converted into the fractional ordinary differential equations,and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients.An efficient backward substitution strategy that was previously provided for a single fractional ordinary differential equation is then used to solve the corresponding systems.The straightforward quasilinearization technique is applied to handle nonlinear issues.Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.
基金supported by the National Natural Science Foundation of China(Grants No.11572111 and 11372097)the 111 Project(Grant No.B12122)
文摘The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling effects of embedded pipes plays an essential role in the design of the structure and its cooling system. In this study, the singular boundary method, a semi-analytical meshless technique, was employed to analyze the temperature distribution. A numerical algorithm solved the transient temperature field with consideration of the effects of cooling pipe specification, isolation of heat of hydration, and ambient temperature. Numerical results are verified through comparison with those of the finite element method, demonstrating that the proposed approach is accurate in the simulation of the thermal field in concrete structures with a water cooling pipe.
文摘In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can significantly reduce the difficulty in the inverse wave source recovery problem,only needing to solve a few equations in the problem domain,since the initial condition/boundary conditions and a supplementary final time condition are satisfied automatically.As a consequence,the eigenfunctions are used to expand the trial solutions,and then a small scale linear system is solved to determine the expansion coefficients from the differencing equations.Because the ill-posedness of the inverse wave source problem is greatly reduced,the present method is accurate and stable against a large noise up to 50%,of which the numerical tests confirm the observation.
基金the National Natural Science Foundation of China(Grant Nos.11975204,11835011,and 12075208)the Natural Science Foundation of Zhejiang Province(Grant No.LY19A050003)the Project of Zhoushan City Science and Technology Bureau(Grant No.2021C21015)。
文摘Starting from a general sixth-order nonlinear wave equation,we present its multiple kink solutions,which are related to the famous Hirota form.We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures.By introducing the velocity resonance mechanism to the multiple kink solutions,we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients.The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited.After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada-Kotera-Caudrey-Dodd-Gibbons(SKCDG)equation,the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.
