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Neural Computing and Applications
Published in: Neural Computing and Applications 8/2018

17-01-2017 | Original Article

The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs

Authors: Omar Abu Arqub, Hasan Rashaideh

Published in: Neural Computing and Applications | Issue 8/2018

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Abstract

Many problems arising in different fields of sciences and engineering can be reduced, by applying some appropriate discretization, either to a system of integrodifferential algebraic equations or to a sequence of such systems. The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of integrodifferential algebraic systems of temporal two-point boundary value problems. Two extended inner product spaces W[0, 1] and H[0, 1] are constructed in which the boundary conditions of the systems are satisfied, while two smooth kernel functions R t (s) and r t (s) are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed.
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Metadata
Title
The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs
Authors
Omar Abu Arqub
Hasan Rashaideh
Publication date
17-01-2017
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 8/2018
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-017-2845-7

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