Pseudo-Spectral Collocation Solution of Nonlinear Time Dependent System of Partial Differential Equations

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 wi...

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Bibliographic Details
Published in:Research Journal of Science and Technology Vol. 9; no. 3; pp. 467 - 471
Main Authors: Shekara, Chandra G., Vishalakshi, T. N.
Format: Journal Article
Language:English
Published: Raipur A&V Publications 01.07.2017
Subjects:
Algorithms
Boundary conditions
Chebyshev approximation
Collocation
Differential equations
Dirichlet problem
Error analysis
Finite difference method
Mathematical models
Nonlinear systems
Partial differential equations
Time dependence
ISSN:0975-4393, 2349-2988
Online Access:Get full text
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Summary: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 multi-variables. 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.
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ISSN:0975-4393
2349-2988
DOI:10.5958/2349-2988.2017.00081.X