IJPAM: Volume 98, No. 1 (2015)

TCHEBYCHEV POLYNOMIAL APPROXIMATIONS
FOR $m^{th}$ ORDER BOUNDARY VALUE PROBLEMS

Samir Kumar Bhowmik
Department of Mathematics and Statistics
College of Science
Al Imam Mohammad Ibn Saud Islamic University (IMSIU)
P.O. BOX 90950, 11623 Riyadh, KINGDOM OF SAUDI ARABIA


Abstract. Higher order boundary value problems (BVPs) play an important role modeling various scientific and engineering problems. A general recipe for a $m^{th}$ order BVPs is sparse (for any natural number $m\ge 2$).

In this article we develop an efficient numerical scheme for linear $m^{th}$ order BVPs. First we convert the higher order BVP to a system of first order BVPs. Then we use Tchebychev polynomials to approximate the solution of the BVP as a weighted sum of polynomials. We collocate at Tchebychev clustered grids to generate a system of equations to approximate the weights for the polynomials. The excellency of the numerical scheme is illustrated through some examples.

Received: August 18, 2014

AMS Subject Classification: 65M12, 65M15

Key Words and Phrases: Tchebychev polynomial; spectral collocation method; boundary value problem; numerical approximation

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DOI: 10.12732/ijpam.v98i1.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 1
Pages: 45 - 63


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