A multilevel wavelet collocation method for solving partial differential equations in a finite domain

Abstract A multilevel wavelet collection method for the solution of partial differential equations is developed. Two different approaches of treating general boundary conditions are suggested. Both are based on the wavelet interpolation technique developed in the present research. The first approach uses wavelets as a basis and results in a differential-algebraic system of equations, where the algebraic part arises from boundary 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 the one-dimensional Burgers equation with small viscosity. The solutions are compared with those resulting from the use of other numerical algorithms. The present results indicate that the method is competitive with well-established numerical algorithms.