New sinusoidal basis functions and a neural network approach to solve nonlinear Volterra–Fredholm integral equations

被引：0
作者：
Stefania Tomasiello
Jorge E. Macías-Díaz
Alireza Khastan
Zahra Alijani
机构：
[1] Università degli Studi di Salerno,Consorzio di Ricerca Sistemi ad Agenti (CORISA)
[2] Universidad Autónoma de Aguascalientes,Departamento de Matemáticas y Física
[3] Institute for Advanced Studies,Department of Mathematics
[4] Basic Sciences,Department of Mathematics and Statistics
[5] University of Tartu,undefined
来源：
Neural Computing and Applications | 2019年 / 31卷
关键词：
Nonlinear integral equations; block-pulse functions; sinusoidal basis functions; learning rule;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we present and investigate the analytical properties of a new set of orthogonal basis functions derived from the block-pulse functions. Also, we present a numerical method based on this new class of functions to solve nonlinear Volterra–Fredholm integral equations. In particular, an alternative and efficient method based on the formalism of artificial neural networks is discussed. The efficiency of the mentioned approach is theoretically justified and illustrated through several qualitative and quantitative examples.
引用
收藏
页码：4865 / 4878
页数：13
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