网络出版日期: 2016-05-15
基金资助
Supported by National Natural Science Foundation of China(51174170) and National Science and Technology Project(2011ZX05013006)
A finite difference method for solving nonlinear Volterra integral equation
Online published: 2016-05-15
Supported by
Supported by National Natural Science Foundation of China(51174170) and National Science and Technology Project(2011ZX05013006)
苟斐斐 , 刘建军 , 刘卫东 , 罗莉涛 . 求解非线性伏尔泰拉积分方程的有限差分方法[J]. 中国科学院大学学报, 2016 , 33(3) : 329 -333 . DOI: 10.7523/j.issn.2095-6134.2016.03.007
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.
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