The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations

The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of differential algebraic systems for ordinary differential equations. The reproducing kernel Hilbert space ⊕j=1mW22a,b⊕⊕j=m+1nW_21a,b is constructe...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 39; no. 15; pp. 4549 - 4562
Main Author: Arqub, Omar Abu
Format: Journal Article
Language:English
Published: Freiburg Blackwell Publishing Ltd 01.10.2016
Wiley Subscription Services, Inc
Subjects:
Algebra
Algorithms
Computation
differential algebraic systems
Differential equations
Gram-Schmidt process
Hilbert space
initial value problems
Kernels
Mathematical models
reproducing kernel algorithm
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ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of differential algebraic systems for ordinary differential equations. The reproducing kernel Hilbert space ⊕j=1mW22a,b⊕⊕j=m+1nW_21a,b is constructed in which the initial conditions of the systems are satisfied. While, two 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. Copyright © 2016 John Wiley & Sons, Ltd.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3884