SOLUTION OF FRACTIONAL SCHRODINGER PARABOLIC PARTIAL DIFFERENTIAL EQUATION BY MUNTZ – LEGENDRE POLYNOMIAL METHOD

Abstract

The basic concepts used in this thesis were given, the Laplace transform method was applied to obtain the exact solution of the given problem, and the Muntz-Legendre Polynomial Method was applied for its approximate solution. In this study, the Muntz-Legendre Polynomial Method was applied to solve Fractional Schrödinger Parabolic Partial Differential Equations. The Muntz-Legendre Polynomial Method was calculated by testing the sample problem for the approximate solution of the Fractional order Schrödinger Parabolic Partial Differential Equation based on the given initial values. This approximate solution was then compared to the exact solution. Since the approximate solution obtained in this problem corresponded to the exact solution, the method was seen to be effective and advantageous. Graphs were obtained for both exact and approximate solutions using the Matlab program. However, a problem whose solution is exponential or trigonometric functions may not correspond to the exact solution; this solution is obtained as an approximate solution.