Transition matrix computation and reduction of boundary error using smooth multiwavelet bases

In this paper we discuss about a differential operator modeling using multiwavelets as a tool to solve partial differential equations (PDEs). It has been argued here that the advantages of smooth multiwavelets make them more suitable for solving PDEs by multiwavelet methods. Multiwavelet methods offer resolution at multilevels and higher approximation order in the boundary for a given filter length. Emphasis is given on calculation of a transition matrix for smooth multiwavelet bases. We propose a new multigrid method in conjunction with a transition matrix approach for solving PDEs to reduce the error near the boundary. The method is also applicable for any general boundary condition. Numerical results are discussed for a secondorder PDE.