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.