Solving Parabolic Partial Differential Equations using Modified Bellman s Method with G-Spline Interpolation

The aim of this paper is to approximate the solution of the parabolic partial differential equations (heat equations) using Bellman s method with the cooperation of the G-spline interpolation formula. The partial differential equation will then be changed into a system of the first order ordinary differential equation. The resulting system may be then solved easily by using the fundamental matrix solution. In this paper, the Bellman s method may be considered as a generalization to the usual Bellman s method with an arbitrary ordinary derivative.