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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 19
Edited by: B.H.V. Topping
Paper IV.7

Fourth Order Runge-Kutta Method in 1D for High Gradient Problems

R. Cortell

ETSI de Caminos, Canales y Puertos, Universidad Politecnica de Valencia, Valencia, Spain

Full Bibliographic Reference for this paper
R. Cortell, "Fourth Order Runge-Kutta Method in 1D for High Gradient Problems", in B.H.V. Topping, (Editor), "Developments in Computational Engineering Mechanics", Civil-Comp Press, Edinburgh, UK, pp 121-124, 1993. doi:10.4203/ccp.19.4.7
In this paper, we present numerical studies for problems of diffusion in one dimension with steep gradients. Two examples are given. One is a non-linear problem of diffusion with chemical reaction. The other is a convective-diffusion problem. The solutions are obtained using a Runge-Kutha (R.-K.) method of fourth order with nonconstant values of step size H. The accuracy of the method for situations with steep gradients is demonstrated.

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