Spectral graph wavelet optimized finite difference method for solution of Burger's equation with different boundary conditions

In this paper, spectral graph wavelet optimized finite difference method (SPGWOFD) has been proposed for solving Burger's equation with distinct boundary conditions. Central finite difference approach is utilized for the approximations of the differential operators and the grid on which the numerical solution is obtained is chosen with the help of spectral graph wavelet. Four test problems (with Dirichlet, Periodic, Robin and Neumann's boundary conditions) are considered and the convergence of the technique is checked. For assessing the efficiency of the developed technique, the computational time taken by the developed technique is compared to that of the finite difference method. It has been observed that developed technique is extremely efficient.