The aim of this paper is to obtain the numerical solutions of fractional Volterra integrodifferential equations by the Jacobi spectral collocation method using the Jacobi-Gauss collocation points.We convert the fracti...The aim of this paper is to obtain the numerical solutions of fractional Volterra integrodifferential equations by the Jacobi spectral collocation method using the Jacobi-Gauss collocation points.We convert the fractional order integro-differential equation into integral equation by fractional order integral,and transfer the integro equations into a system of linear equations by the Gausssian quadrature.We furthermore perform the convergence analysis and prove the spectral accuracy of the proposed method in L∞norm.Two numerical examples demonstrate the high accuracy and fast convergence of the method at last.展开更多
This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel p（t, s） = （t - s）^-μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 20...This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel p（t, s） = （t - s）^-μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233：938 950], the error analysis for this approach is carried out for 0 〈 μ 〈 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i.e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-ype but also establish the error estimates under a more general regularity assumption on the exact solution.展开更多
The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gau...The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.展开更多
基金This work is supported by the National Natural Science Foundation of China(Grant Nos.11701358,11774218)。
文摘The aim of this paper is to obtain the numerical solutions of fractional Volterra integrodifferential equations by the Jacobi spectral collocation method using the Jacobi-Gauss collocation points.We convert the fractional order integro-differential equation into integral equation by fractional order integral,and transfer the integro equations into a system of linear equations by the Gausssian quadrature.We furthermore perform the convergence analysis and prove the spectral accuracy of the proposed method in L∞norm.Two numerical examples demonstrate the high accuracy and fast convergence of the method at last.
文摘This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel p（t, s） = （t - s）^-μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233：938 950], the error analysis for this approach is carried out for 0 〈 μ 〈 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i.e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-ype but also establish the error estimates under a more general regularity assumption on the exact solution.
基金This work is supported by the National Natural Science Foundation of China(Grant Nos.11701358,11774218)。
文摘The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.
