Second-generation wavelet optimized finite difference method (SGWOFD) for solution of Burger’s equation with different boundary conditions

Abstract

In this paper, second-generation wavelet optimized finite difference method (SGWOFD) is developed for solution of Burger’s equation with different boundary conditions. The viscid Burger’s equation is considered with periodic, Dirichlet, Neumann and Robin’s boundary conditions. For the approximations of the differential operators, central finite difference scheme has been used and Crank Nicolson’s scheme is used for the time integration. Numerical solutions have been optimized on an adaptive grid which is generated using the second-generation wavelet. The beauty of the second-generation wavelet is that its construction is not affected by the boundary conditions. For each test problem, the convergence of the method has been verified. The CPU time taken by SGWOFD has been computed for each test problem and is compared with the CPU time taken by the finite difference method on a uniform grid. It has been revealed that SGWOFD is highly efficient.