MATLAB EVALUATION OF THE m,n (x)
C. I. Popovici · 2010
After approaching the problem of the numerical solution of Stefan’s Problem by Finite Element Methods (FEM) or by Finite Difference Methods in his earlier papers [5]-[11], the author goes on with using the wavelet - Galerkin method for the solution of the earlier mentioned problem. The evaluation of the coefficients m,n j,k (x) is a first step in the numerical approximation of the Navier - Stokes equation, of the problem with free boundary of Stefan type, etc. This paper is one in a set of articles dealing with solutions to PDEs or ODEs using the wavelet - Galerkin method. In order to approximate the solution, a couple of families of coefficients are needed; they occur in wavelet series and they are involved in discretizing differential equations that characterize mathematical-mechanical models. Following some earlier ideas (of references [1],[2],[3],[4],[12],[13],[14]), we have worked out several algorithms and MATLAB - based programs that differ from the algorithms in [2], allowing to obtain high precision results for the necessary functionals. The accuracy of the results follows from the performances of the MATLAB programming environment. In this paper it is described the MATLAB evaluation of the integral m,n j,k (x) = Z x 0 �(y)� (m) (y j)� (n) (y k)dy. The orthonormal wavelet class with compact support, developed by Daubechies (in 1988) follows to be adapted as a Galerkin basis in the space domain.