Hermite Interpolant Multiscaling Functions for Numerical Solution of the Convection Diffusion Equations

A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diffusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diffusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.