Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method

Ghaleb Gumah, Khaled Moaddy, Mohammed Al-Smadi, Ishak Hashim

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.

Original languageEnglish
Article number2920463
JournalJournal of Function Spaces
Volume2016
DOIs
Publication statusPublished - 2016

Fingerprint

Reproducing Kernel Hilbert Space
Volterra Integral Equations
Kernel Function
Integral Equations
Analytical Solution
Orthogonal Basis
Reproducing Kernel
Computational Experiments
Summation
Hilbert space
Physics
Engineering
Numerical Results
Series
Methodology
Term
Approximation
Demonstrate
Strategy
Form

ASJC Scopus subject areas

  • Analysis

Cite this

Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method. / Gumah, Ghaleb; Moaddy, Khaled; Al-Smadi, Mohammed; Hashim, Ishak.

In: Journal of Function Spaces, Vol. 2016, 2920463, 2016.

Research output: Contribution to journalArticle

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