A time two-grid algorithm for the two dimensional nonlinear PIDE with a weakly singular kernel
A time two-grid algorithm for the two dimensional nonlinear PIDE with a weakly singular kernel
复制标题
弱奇异核二维非线性分数阶PIDE的时间二网格算法
DOI：
10.1016/j.matcom.2022.03.004
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发表时间：
2022
影响因子：
4.6
通讯作者：
Lijiao Wu
中科院分区：
文献类型：
--
作者：
Furong Wang;Xuehua Yang;Haixiang Zhang;Lijiao Wu
本文的主要目的是用时间双网格有限差分(FD)算法求解具有弱奇异核的二维非线性分数次偏积分-微分方程(PIDE)。时间上采用二阶后向差分公式(BDF)和L1格式。为了提高非线性系统的求解效率，构造了时间双网格算法。在粗网格上用牛顿迭代法求解非线性离散方程组，在细网格上用拉格朗日线性插值法求出构造差分格式所需的函数值。在空间上采用二阶有限差分方法。证明了两网格全离散系统的无条件稳定性和收敛性。数值实验表明，与求解非线性系统的一般有限差分方法相比，本文提出的两网格数值算法所用的CPU时间较少。
The main aim of this paper is to solve the two-dimensional nonlinear fractional partial integro-differential equation (PIDE) with a weakly singular kernel by using the time two-grid finite difference (FD) algorithm. The second-order backward difference formula (BDF) and L1 scheme are used in time. The time two-grid algorithm is constructed to improve the solving efficiency of nonlinear systems. The Newton iteration is used to solve nonlinear discrete system on the coarse grid, and then we apply Lagrangian linear interpolation to attain the function value used in constructing the difference scheme on the fine grid. The second-order finite difference method (FDM) is used in space. The unconditional stability and convergence are attained for the two-grid fully discrete system. Numerical experiments show that the used CPU time for the presented two-grid numerical algorithm is lower than the general finite difference method for solving the nonlinear system.