THE INTERPOLATORY WAVELETS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

Abstract

In this work we present a hybrid scheme combining the meted-of-line with interpolatory wavelets and central finite differences to solve numerically some nonlinear evolution partial differential equations, (PDEs), with soliton type solutions. The employment of the interpolatory wavelets permits, in this case, to significatively reduce the number of nodes of the non-uniform moving grid. Consequently an important reduction of the order of the resulting stiff ODE system is obtained. Some numerical tests are presented solving the Schrödinger equation, which models important physical phenomena nowadays