New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations
Joint Authors
Khalil, Hammad
Khan, Rahmat Ali
Source
Chinese Journal of Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-13
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We study Legendre polynomials and develop new operational matrix of integration.
Based on the operational matrix, we develop a new method to solve a coupled system of Fredholm integral equations of the form U(x)+λ11∫01K11(x,t)U(t)dt+λ12∫01K12(x,t)V(t)dt=f(x), V(x)+λ21∫01K21(x,t)U(t)dt+λ22∫01K22(x,t)V(t)dt=g(x), where λ11, λ12, λ21, and λ22 are real constants and f,g∈C([0,1]).
The method reduces the coupled system to a system of easily solvable algebraic equations without discretizing the original system.
As an application, we provide examples and numerical simulations demonstrating that the results obtained using the new technique match very well with the exact solutions of the problems.
To show the efficiency of the method, we compare our results with some of the results already studied with other available methods in the literature.
American Psychological Association (APA)
Khalil, Hammad& Khan, Rahmat Ali. 2014. New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations. Chinese Journal of Mathematics،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-449362
Modern Language Association (MLA)
Khalil, Hammad& Khan, Rahmat Ali. New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations. Chinese Journal of Mathematics No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-449362
American Medical Association (AMA)
Khalil, Hammad& Khan, Rahmat Ali. New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations. Chinese Journal of Mathematics. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-449362
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-449362