IJPAM: Volume 96, No. 4 (2014)

A STIFFLY STABLE SECOND DERIVATIVE BLOCK
MULTISTEP FORMULA WITH CHEBYSHEV
COLLOCATION POINTS FOR STIFF PROBLEMS

J.O. Ehigie$^1$, S.A. Okunuga$^2$
$^{1,2}$Department of Mathematics
University of Lagos
Dan Fodio Blvd, Lagos 23401, NIGERIA


Abstract. Most block methods in the literature which are implemented in predictor-corrector mode, usually suffer some stability setbacks and this may hinder their implementation on some stiff problems.

In this paper, we construct a stiffly stable block second derivative backward differentiation formula with Chebyshev collocation points that is self-starting and is capable of solving stiff problems. The method is applied in block form as a simultaneous numerical integrator over non-overlapping subintervals. The method is proven to possess stiffly stable, $A_0$ stable and $A(\alpha)$ stable properties. Some numerical examples reveal that this class of methods is very promising and are suitable for solving stiff problems. 65L05, 65L06

Received: March 7, 2014

AMS Subject Classification: 65L05, 65L06

Key Words and Phrases: stiffly stable, Chebyshev collocation points, stiff problems, second derivative backward differentiation formula

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DOI: 10.12732/ijpam.v96i4.4 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: 2014
Volume: 96
Issue: 4
Pages: 457 - 481


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