关键词: 伏尔泰拉积分方程, 非线性, 数值差分方法, 误差分析

Abstract:

A new numerical solution is provided for Volterra integral equation of the second kind. The integral equation is discretized by numerical difference method and is then formulated as nonlinear algebraic equations, which is solved by iteration approach. Thus the numerical solution for this kind of Volterra Integral equation is provided. The accuracy of the proposed approach is analyzed and is proved to reach the order of Δt², which meets the need of engineering computation. A case study is provided to verify the feasibility of the method. The difference between the numerical solution and the analytical solution is about 10^-5. If numerical differential method with higher order is applied to discretize the integral equation, results of higher order accuracy will be obtained.

Key words: Volterra integral equation, non-linear, numerical finite diference method, tolerance analysis