Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 14, Issue 3, Pages 760-769Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2007.11.004
Keywords
Numerical solutions; Chebyshev spectral collocation method; Convection-diffusion equations; Burgers' equation; Modified Burgers' equation
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The method of El-Gendi [El-Gendi SE. Chebyshev solution of differential integral and integro-differential equations. J Comput 1969;12:282-7; Mihaila B, Mihaila I. Numerical approximation using Chebyshev polynomial expansions: El-gendi's method revisited. J Phys A Math Gen 2002;35:731-46] is presented with interface points to deal with linear and non-linear convection-diffusion equations. The linear problem is reduced to two systems of ordinary differential equations. And, then, each system is solved using three-level time scheme. The non-linear problem is reduced to three systems of ordinary differential. Each one of these systems is, then, solved using three-level time scheme. Numerical results for Burgers' equation and modified Burgers' equation are shown and compared with other methods. The numerical results are found to be in good agreement with the exact solutions. (C) 2007 Elsevier B.V. All rights reserved.
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