Third Order Backward Difference Formula for a First Order Stiff System in Piecewise Uniform Mesh

B. Sumithra

doi:https://doi.org/10.14445/22315373/IJMTT-V33P535

International Journal of Mathematics Trends and Technology

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Volume 33 | Number 4 | Year 2016 | Article Id. IJMTT-V33P535 | DOI : https://doi.org/10.14445/22315373/IJMTT-V33P535

Third Order Backward Difference Formula for a First Order Stiff System in Piecewise Uniform Mesh

B. Sumithra

Abstract

Stiff system of Ordinary Differential Equations can be exemplified by problems in chemical kinetics, fluid dynamics, quantum mechanics, electrical networks, etc. In this paper, a third order Backward Differentiation Formula (BDF-3) is suggested on a piecewise uniform mesh(PUM) to solve a system of first order stiff Ordinary Differential Equations(ODEs). It is proved that the numerical approximations generated by this method with PUM produce numerical solutions with less computational effort and less error as compared to the method without PUM. Numerical results are presented in support of the theory.

Keywords

System of stiff differential equations, Initial value problem, BDF-3, Piecewise uniform mesh.

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Citation :

B. Sumithra, "Third Order Backward Difference Formula for a First Order Stiff System in Piecewise Uniform Mesh," International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 4, pp. 268-275, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V33P535