WAVELET-BASED SOLUTION TO TIME-DEPENDENT TWO-POINT INITIAL BOUNDARY VALUE PROBLEMS WITH NON-PERIODIC BOUNDARY CONDITIONS INVOLVING HYPERBOLIC EQUATIONS

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 wavelet-based Galerkin's solution to time dependent two-point initial-boundary-value problems in Hyperbolic Equations with non-periodic boundary 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 to non-periodic initial-boundary-value-problems, we extend our prior research of solution of parabolic problems to a hyperbolic problem. The results of the wavelet solution are examined and they are found to compare favorably to the exact solution. This paper on the whole indicates that the wavelet technique is a strong contender for an approximate solution to two point initial boundary value problems in hyperbolic equations with non-periodic conditions.