Pseudo-Spectral Collocation Solution of Nonlinear Time Dependent System of Partial Differential Equations - Shekara, Chandra G.; Vishalakshi, T. N. (Research Journal of Science and Technology, 2017)
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.