Volterra型微分-积分方程的数值格式构造及理论分析

Numerical Scheme Construction and TheoreticalAnalysis for Integral-Differential Equations of Volterra Type

本文研究了一类Volterra型微分-积分方程的数值格式构造及其理论分析.格式构造方面,利用有限差分方法进行时间和空间离散,对于积分项采用复合梯形求积公式进行处理.最后,给出了数值格式的稳定性分析和误差估计,其误差的收敛阶为Ο(τ+h^(4)),其中τ为时间步长,h为空间步长.

In this paper,a numerical scheme construction and theoretical analysis was mainly developed for solving the Volterra integral-differential equations.In terms of scheme construction,the finite difference approximation issued for time and space derivative,and the compound trapezoidal quadrature formula issued for integral term.Finally,the unconditional stability and convergence were given.In addition,the error analysis was carried out,which showed that the convergence order was O(ι+h^(4)),whereιwas the time step,and h was the space step.