Paper Info
Title
The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs.
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.
Year
DOI
Venue
2018
10.1007/s00521-017-2845-7
Neural Computing and Applications
Keywords
Field
DocType
Integrodifferential algebraic systems, Temporal boundary value problems, Reproducing kernel theory, Volterra operator
Boundary value problem,Discretization,Mathematical optimization,Algebraic number,Volterra operator,Mathematical analysis,Inner product space,Algebraic equation,Mathematics,Reproducing kernel Hilbert space,Kernel (statistics)
Journal
Volume
Issue
ISSN
30
8
1433-3058
Citations 
PageRank 
References 
4
0.41
25
Authors
2
Name
Order
Citations
PageRank
Omar Abu Arqub180.85
Hasan Rashaideh2112.30