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The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations
Author(s) -
Arqub Omar Abu
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3884
Subject(s) - mathematics , reproducing kernel hilbert space , kernel (algebra) , ordinary differential equation , representer theorem , hilbert space , algorithm , differential equation , kernel method , algebra over a field , kernel embedding of distributions , mathematical analysis , computer science , discrete mathematics , pure mathematics , artificial intelligence , support vector machine
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 = 1 mW 2 2a , b⊕⊕ j = m + 1 nW _2 1a , bis 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.