Wavelet-Based Solution to Time-Dependent Non-Linear Two-Point Initial Boundary Value Problems with Non-Periodic Boundary Conditions Involving Composite Media

摘要

The Wavelet solution for boundary-value problems is relatively new and has been mainly restricted to the solutions in data compression, image processing and recently to the solution of differential equations with periodic boundary conditions. This paper is concerned with the Galerkin's solution to time dependent composite-media non-linear two-point initial-boundary-value problems with non-periodic conditions. The wavelet method can offer several advantages in solving the initial-boundary-value problems than the traditional methods such as Fourier series, Finite Differences and Finite Elements by reducing the computational time near singularities because of its multi-resolution character. In order to demonstrate the wavelet technique, we extend our prior research of solution to parabolic equations and problems with nonlinear boundary conditions to problems involving Composite Media which are symmetrically located. The results of the wavelet solutions are examined and they are found to compare favorably to the known exact solution. Furthermore, various wavelet solutions have been plotted varying diffusivities and boundary temperatures. This paper on the whole indicates that the wavelet technique is a strong contender for solving partial differential equations with non-periodic conditions.