On The Numerical Solutions of a Class of Singular Integro-Differential Equations

摘要

We consider a class of singular integro-differential equations with nonatomic difference operators and extend the results in paper [8]. For this specific type of integro-differential equations, it can be transformed into first order hyperbolic partial differential equations. By applying nonconforming finite element methods on space and keeping time as a variable, we establish a semi-discrete scheme. We then use an ordinary differential equation solver for the semi-discrete scheme. Furthermore, by discretizing both space and time, we extend the semi-discrete scheme to a full-discrete scheme which is the method in [8, 9]. However, the observation in [8, 9] about rates of convergence by uniform mesh was not convincing enough. In this paper, we report our different numerical findings and comment on the rates of convergence.