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https://hdl.handle.net/11499/6131
Title: | Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM) | Authors: | Gürarslan, Gürhan Sarı, Murat |
Keywords: | Differential quadrature (DQ) Diffusion equation Nonlinear PDE Runge-Kutta method Strong stability preserving Alternative methods Approximate solution Differential quadrature Differential quadrature methods Exact solution Non linear PDE Nonlinear diffusion equations Nonlinear partial differential equations Numerical errors Numerical solution Physical model Runge-Kutta Storage spaces Differentiation (calculus) Diffusion Models Numerical methods Partial differential equations Runge Kutta methods Nonlinear equations |
Abstract: | In this work, accurate solutions to linear and nonlinear diffusion equations were introduced. A polynomial-based differential quadrature scheme in space and a strong stability preserving Runge-Kutta scheme in time have been combined for solving these equations. This scheme needs less storage space, as opposed to conventional numerical methods, and causes less accumulation of numerical errors. The results computed by this way have been compared with the exact solutions to show the accuracy of the method. The approximate solutions to the nonlinear equation have been computed without transforming the equation and without using the linearization. The present results are seen to be a very reliable alternative method to the existing techniques for the problems. In order to obtain physical models much closer to the nature, this procedure has a potential to be used to other nonlinear partial differential equations. © 2009 John Wiley & Sons, Ltd. | URI: | https://hdl.handle.net/11499/6131 https://doi.org/10.1002/cnm.1292 |
ISSN: | 2040-7939 |
Appears in Collections: | Fen-Edebiyat Fakültesi Koleksiyonu Mühendislik Fakültesi Koleksiyonu Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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