A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

Document Type : Original Article

Authors
Behnam Sepehrian 1 ΒΆ
Mohsen Razzaghi 2
1 Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
2 Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
10.29252/maco.1.2.6
Abstract
In this article, the properties of single-term Walsh series are presented and utilized for solving the nonlinear Volterra-Hammerstein integral equations of second kind. The interval [0;1) is divided tomequal subintervals,mis a positive integer number. The midpoint of each subinterval is chosen as a suitable collocation point. By the method the computations of integral equations reduce into some nonlinear algebraic equations. The method is computationally attractive, and gives a continuous approximate solution. An analysis for the convergence of method is presented.The efficiency and accuracy of the method are demonstrated through illustrative examples. Some comparisons aremade with the existing results.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 1, Issue 2
December 2020
Pages 59-69