Approximation of Burger Equation by Orthogonal Collocation Method With Base Shifted Jacobi Polynomials P_n~((α,β)) for Different Values of α and β

摘要

In the present study, orthogonal collocation method has been followed to discretize the non-linear Burger equation. Shifted Jacobi polynomials P_n~((α,β))(x) has been chosen as base functions. The problem is approximated for different values of α and β. Numerical values obtained for different values of α and β have been compared to the exact ones. The stability analysis has been done by von Neumann approach. The technique is found to be unconditionally stable for any choice of base function.