Quasi-wavelet solution of diffusion problems

摘要

A new method, quasi-wavelet method, is introduced for solving partial differential equations of diffusion which are important to chemical and mechanical engineering. A new scheme for the extension of boundary conditions is proposed. The quasi-wavelet method is utilized to discretize the spatial derivatives, while the Runge-Kutta scheme is employed for the time advancing. The problems of particle diffusion in the electrochemistry reaction and temperature diffusion in plates are studied. Quasi-wavelet solution of the former problem is compared with those of a finite difference method. Solution of the latter problem is calibrated by analytical solution. Numerical results indicate that the quasi-wavelet approach is very robust and efficient for diffusion problems.