Solution of Two Point Boundary Value Problems Using Wavelet Integrals

Abstract In this paper, we obtain some special types of integrals of Daubechies Wavelets which are used as Galerkin basis functions for numerical solution of partial differential equations of one dimension. Galerkin bases are constructed by integrating Daubechies functions which are compactly supported and which constitute an orthonormal basis of L2(R). Theoretical and numerical results are obtained for elliptic problems of second order with different types of boundary conditions. Optimal error estimates are also obtained. Comparison of solutions with simple finite difference method suggests that for this class of problems, the present method will provide a better alternative to other classical methods. The methodology can be generalized to multidimensional problems by taking care of some technical facts.