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Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae
American Journal of Mathematical and Computer Modelling
Volume 2, Issue 4, November 2017, Pages: 103-116
Received: Sep. 18, 2017; Accepted: Oct. 9, 2017; Published: Nov. 8, 2017
Authors
Yohanna Sani Awari, Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria
Micah Geoffrey Kumleng, Department of Mathematics, University of Jos, Jos, Nigeria
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Abstract
The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDF). In this paper, we focus on the derivation of the fourth, sixth and eighth order extended trapezoidal rule of first kind (ETRs) formulae through Hermite polynomial as basis function which we named FETR, SETR and EETR respectively. We then interpolate and collocate at some points of interest to generate the desire method. The stability analysis on our methods suggests that they are not only convergent but possess regions suitable for the solution of stiff ordinary differential equations (ODEs). The methods were very efficient when implemented in block form, they tend to perform better over existing methods.
Keywords
Stiffness, Hermite Polynomial, ETRs, A-Stability, Ordinary Differential Equations
Yohanna Sani Awari, Micah Geoffrey Kumleng, Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae, American Journal of Mathematical and Computer Modelling. Vol. 2, No. 4, 2017, pp. 103-116. doi: 10.11648/j.ajmcm.20170204.13
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