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

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. T...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 69; no. 4; pp. 3131 - 3149
Main Authors: Dai, Xuefei, Niu, Jing, Xu, Yanxin
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Integral equations
Least squares
Linear algebra
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Noise control
Numerical analysis
Original Research
Polynomials
Theory of Computation
Volterra integral equations
65R20
Reproducing kernel space
Quasi-Newton’s method
Least-square method
33F05
Nonlinear Volterra integral equation
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary: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 nonlinear 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 ε -approximate solution and its convergence. Finally, we illustrate the accuracy and reliability of this method by giving some examples.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-023-01874-8