Open Access
Subscription Access
Open Access
Subscription Access
Pseudo-Spectral Collocation Solution of Nonlinear Time Dependent System of Partial Differential Equations
Subscribe/Renew Journal
The pseudo-spectral collocation solution of time dependent nonlinear system of partial differential equations with Dirichlet’s boundary conditions is presented in this paper. The nonlinear systems of partial differential equations are reduced to linear form by using quasi-linearization along with the Taylor’s series of multivariables. Then the spectral collocation algorithm is developed by using Lagrange interpolating polynomials as basis of the solution at the Chebyshev-Gauss-Labatto grid points. This algorithm is implemented using MATLAB for test case problems and the results are presented graphically. Error analysis is done by comparing the numerical solution and analytical solution. Solution found by the said method is more accurate compared to the finite difference method with uniform grid points.
Keywords
Pseudo-Spectral, Chebyshev-Collocation, Lagrange’s-Interpolation, Quasi-Linearization, Gauss-Labatto Points, Taylor’s-Series.
Subscription
Login to verify subscription
User
Font Size
Information
- M. A. Abdou, A.A Soliman, variational iteration method for solving Burger’s and coupled Burger’s equation, Journal of compuational and applied mathematics, vol.181, 2005, pp. 245-251.
- C. Canuto, A. Quarteroni, M.Y. Hussaini and T. Zang, Spectral methods in fluid mechanics, Springer-Verlag, New York, 1988.
- M.T. Darvishi, F. Ghoreshi, Error reduction for higher derivatives of chebyshev collocation method using preconditioning and domain decomposition, Korean J. Comput. Math. Vol.6(2),1999, pp.421-435.
- M.T. Darvishi, M. Javidi, A numerical solution of Burger’s equation by pseudospectral method and Darvishi’s preconditionaing, Appl. Math. Comput., vol.173(1), 2006, pp.421-429.
- W.S. Don, A. Solomoff, Accuracy and speed in computing the chebyshev collocation derivatives, SIAM J. Sci. Comput., vol.16(4), 1995, pp.1253-1268.
- M. Javidi, Spectral collocation method for the solution of the generalized Burger’s –Fisher equation, Appl.Math. Comput., vol.174(1), 2006, pp.129-141.
- M. Javidi, A numerical solution for nonlinear PDEs, Int.Contemp.Math.Sciences, vol.2(8), 2007, pp.373-381.
- L.N. Trefethen, Spectral methods in MATLAB, SIAM, Philadelphia, 2000.
- S.S. Motsa, V.M. Magagula and P. Sibanda, A Bivariate chebyshev spectral collocation quasilinearization method for nonlinear evolution of parabolic equation, The scientific world journal, vol.2014, pp.13.
- U.N. Nowak, A fully adaptive MOL-treatment of parabolic 1-D problems with extrapolation techniques, Appl. Numer. Math., vol.20, 1996, pp.129-141.
- G. Chandra Shekara, “Spectral collocation solution of non-linear time dependent partial differential equation with nonlinear boundary conditions,” Procedings of International conference on Fluid Dynamics and its Applications, 2017.
Abstract Views: 195
PDF Views: 0