ON THE WAVELET METHODS TO SOLVE PERTURBATION BOUNDARY VALUE ROBLEMS

In this paper we present our numerical results to insure the improvement on the performance of PASVA algorithm to solve perturbation two-point boundary value problems, by using wavelet method in the inner loop of the nonlinear solver. Introduction Two point boundary value problems (TPBVP) arise naturally in the process of solving partial differential equations. Methods based on shooting, finite difference and collocation are well known in the literature and well represented also in standard software. Methods based on wavelet representation of the solution are relatively new and may very much be dependent on the type of wavelet to be used. We select several standard TPBVP problems, run our wavelet algorithm and compare its performance and results to those obtainable from PASVA. As a standard algorithm PASVA is well known for its outstanding performance on nonperturbation and mildly perturbation ordinary differential equations, while wavelets (considering their rich variety and neat representation) allow new ideas to be incorporated in order to enhance the performance of existing software. This paper documents preliminary results of our numerical experiments. Two-point Boundary Value Problems (TPBVP) We consider the general TPBVP u'(t) = f(t,u) in t ∈ [a,b] r(u(a),u(b)) = 0. (1) The currently accepted standard practice is to approximate it by a set of nonlinear algebraic equations in the following sense. In the interval [a,b],