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Research Journal of Science and Technology
ISSN: 2349-2988(Online), 0975-4393(Print)
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Pseudo-Spectral Collocation Solution of Nonlinear Time Dependent System of Partial Differential Equations
Chandra Shekara G.
T. N. Vishalakshi
Chandra Shekara G., T. N. Vishalakshi
Department of Mathematics, B .M.S. College of Engineering, Bangalore, Karnataka, India
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.
Pseudo-Spectral, Chebyshev-Collocation, Lagrange’s-Interpolation, Quasi-linearization, Gauss-Labatto points, Taylor’s-series.
Chandra Shekara G., T. N. Vishalakshi. Pseudo-Spectral Collocation Solution of Nonlinear Time Dependent System of Partial Differential Equations. Research J. Science and Tech. 2017; 9(3): 467-471.
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