Wavelet Solution of Convection-Diffusion Equation with Neumann Boundary Conditions

In this paper, we derive a highly accurate numerical method for the solution of one-dimensional convection-diffusion equation with Neumann boundary conditions. This parabolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method and the time variable is discretized by using various classical finite difference schemes. The numerical results show that this method gives high favourable accuracy compared with the exact solution.