Analysis of Two-Level Mesh Method for Partial IntegroDifferential Equation

被引：0
作者：
Tang, Quan [1 ]
Luo, Ziyang [1 ]
Zhang, Xindong [1 ]
Liu, Juan [2 ]
机构：
[1] Xinjiang Normal Univ, Sch Math Sci, Urumqi 800017, Peoples R China
[2] Guizhou Univ Finance & Econ, Coll Big Data Stat, Guiyang 550025, Peoples R China
来源：
JOURNAL OF FUNCTION SPACES | 2022年 / 2022卷
基金：
中国国家自然科学基金;
关键词：
IMPLICIT DIFFERENCE SCHEME; HEAT-CONDUCTION; COLLOCATION METHODS; DISCRETIZATION; MODEL;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. For the first step, we use finite difference method in time and global radial basis function (RBF) finite difference (FD) in space. For the second step, we use the finite difference method to solve the proposed problem. This twolevel mesh scheme is obtained by combining the radial basis function with finite difference. We prove the stability and convergence of scheme and show that the convergence order is O(tau(2) + h(2))THORN, where t and h are the time step size and space step size, respectively. The results of numerical examples are compared with analytical solutions to show the efficiency of proposed scheme. The numerical results are in good agreement with theoretical ones.
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页数：10
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