Numerical Solutions of Fredholm Integral Equations using Collocation-Tau Method
Domingo, Augustine ‘Dele
Domingo, Augustine ‘Dele, Mathematics, Physics, and Information Technology Department, University of Belize, Belmopan, Belize.
Manuscript received on April 01, 2015. | Revised Version Manuscript Received on April 23, 2015. | Manuscript published on April 20, 2015. | PP: 8-13 | Volume-1 Issue-5, April 2015
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Abstract: Many problems arising in mathematics and in particular, applied mathematics or mathematical physics can be formulated in two but related ways, namely as differential or integral equation. Not all of such equations can be solved analytically; hence, numerical techniques are desirable. A tau collocation approach that combines the tau method with the idea of collocation for the solution of integral equations of Fredholm type is considered herein. The scope of the Lanczoz-Tau method is thus extended so that integral equations can also be solved numerically with the tau process. This work is supported with numerical evidences which show that the desired solution is accurately estimated by the resulting Tau approximant.
Keywords: Collocation-Tau method, Fredholm Integral equations, Chebyshev polynomials, Linear Ordinary Differential equations.