International Journal of Bioinformatics and Biomedical Engineering

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Robust Numerical Solution of the Time-Dependent Problems with Blow-Up

Pages: 53-63 Views: 1486 Downloads: 909

[01]
Kolade M. Owolabi, Department of Mathematical Sciences, Federal University of Technology, Ondo-State, Nigeria; Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, Republic of South Africa.

Numerical solutions of nonlinear time-dependent partial differential equations with blow-up are considered in this paper. Such systems of PDEs are categorized into linear and nonlinear parts to allow the use of two classic mathematical ideas in space and time. The main focus in this paper is to discretized in space with higher order finite difference approximation and integrate the resulting nonlinear ordinary differential equations with an adaptive fourth-order exponential time differencing Runge-Kutta (ETDRK4) scheme. Stability analysis of the scheme is also examined. This paper is primarily concerned with the use of the ETDRK4 method to simulate some of the blow-up phenomena in nonlinear parabolic equations that are largely encountered in a number of physical situations, like chemical reaction-diffusion, electrical heating, fluid flow and population growth. It is expected that the time at which blow-up occurs will reflect in the numerical results.

Blow-Up Problems, Exponential Time Differencing Methods, Nonlinear, Time-Dependent Pdes, Stability

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