Please use this identifier to cite or link to this item: 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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