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Fourth-Order Time Stepping for Stiff PDEs via Integrating Factor

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The usual technique of numerical solutions of ordinary differential equations (ODE) consists of several fragments that were formed during a long period of time in order to find solutions for the equations. The method like Runge-Kutta that was well established is still being used as the basis of many efficient codes. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This study overcomes such problems via the exponential method. In the first part of this paper, the exponential time differencing Runge-Kutta 4 method (ETDRK4) is used to solve the diagonal example of Kuramoto-Sivashinsky (K-S) equation. The second part is to solve Korteweg-de Vries (KdV) equation with Fourier transformation, and together with implementation of integrating factor method.
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Document Type: Research Article

Publication date: 01 January 2013

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  • ADVANCED SCIENCE LETTERS is an international peer-reviewed journal with a very wide-ranging coverage, consolidates research activities in all areas of (1) Physical Sciences, (2) Biological Sciences, (3) Mathematical Sciences, (4) Engineering, (5) Computer and Information Sciences, and (6) Geosciences to publish original short communications, full research papers and timely brief (mini) reviews with authors photo and biography encompassing the basic and applied research and current developments in educational aspects of these scientific areas.
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