带有弱奇异核的四阶偏积分微分方程的Sinc-Galerkin方法

The Sinc-Galerkin Method for the Fourth-Order Partial Integro-Differential Equation with Weakly Singular Kernels

本文我们利用Sinc-Galerkin方法求解带有弱奇异核的四阶偏积分微分方程。首先在时间上借助L1格式和梯形卷积求积公式分别离散分数阶导数和积分,其次在空间上利用Sinc-Galerkin方法近似四阶偏导项,得到方程的全离散格式。最后推导出数值格式的收敛阶并通过数值算例来验证该方法的准确性和有效性。

The Sinc-Galerkin method is considered and analyzed for solving the fourth-order partial integro-differential equation with weakly singular kernels. At first, for the temporal direction, we use L1 scheme to approximate Caputo derivative and the trapezoidal convolution quadrature rule to discretize the Riemann-Liouville fractional integral term. Then for space, we utilize Sinc-Galerkin method to deal with fourth-order partial derivative and obtain the fully discrete scheme. Finally, we deduce the convergence order of the numerical scheme and verify the accuracy and effectiveness of the proposed method through a numerical example.