A MULTILEVEL WAVELET COLLOCATION METHOD FOR SOLVING PARTIAL-DIFFERENTIAL EQUATIONS IN A FINITE DOMAIN

A multilevel wavelet collection method for the solution of partial dif ferential equations is developed. Two different approaches of treating general boundary conditions are suggested. Both are based on the wave let interpolation technique developed in the present research. The fir st approach uses wavelets as a basis and results in a differential-alg ebraic system of equations, where the algebraic part arises from bound ary conditions. The second approach utilizes extended wavelets, which satisfy boundary conditions exactly. This approach results in a system of coupled ordinary differential equations. The method is tested on t he one-dimensional Burgers equation with small viscosity. The solution s are compared with those resulting from the use of other numerical al gorithms. The present results indicate that the method is competitive with well-established numerical algorithms. (C) 1995 Academic Press, I nc.