An efficient numerical algorithm for solving nonlinear Volterra integral equations in the reproducing kernel space

被引:2
作者
Dai, Xuefei [1 ]
Niu, Jing [1 ]
Xu, Yanxin [1 ]
机构
[1] Harbin Normal Univ, Harbin 150025, Heilongjiang, Peoples R China
关键词
Nonlinear Volterra integral equation; Reproducing kernel space; Least-square method; Quasi-Newton's method; BLOCK-PULSE FUNCTIONS; INTEGRODIFFERENTIAL EQUATIONS; SYSTEMS; HYBRID; KIND;
D O I
10.1007/s12190-023-01874-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main purpose of this paper is to approximate the solution of the nonlinear Volterra integral equation numerically in the reproducing kernel space. Consequently, in the study, combining Quasi-Newton's method and the least-square method, we develop a new method for solving this kind of equation. This technique transforms the non-linear Volterra integral equation into a linear algebraic system of equations, which can be solved by using the least-square method breezily. At the same time, to ensure the preciseness of the method, we strictly analyze the existence and uniqueness of e-approximate solution and its convergence. Finally, we illustrate the accuracy and reliability of this method by giving some examples.
引用
收藏
页码:3131 / 3149
页数:19
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