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Calcolo
Published in: Calcolo 3/2018

01-09-2018

Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm

Author: Omar Abu Arqub

Published in: Calcolo | Issue 3/2018

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Abstract

The aim of the present analysis is to implement a relatively recent computational algorithm, reproducing kernel Hilbert space, for obtaining the solutions of systems of first-order, two-point boundary value problems for ordinary differential equations. The reproducing kernel Hilbert space is constructed in which the initial–final conditions of the systems are satisfied. Whilst, three smooth kernel functions 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. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems compared with other numerical methods.
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Metadata
Title
Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm
Author
Omar Abu Arqub
Publication date
01-09-2018
Publisher
Springer International Publishing
Published in
Calcolo / Issue 3/2018
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-018-0274-3

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