Non-polynomial Spline Solution for a Fourth-Order Non-homogeneous Parabolic Partial Differential Equation with a Separated Boundary Condition

Abstract

In this paper, a fourth-order non-homogeneous parabolic partial differential equation with initial and separated boundary conditions is solved by using a non-polynomial spline method. In the solution of the problem, finite difference discretization in time, and parametric quintic spline along the spatial coordinate have been carried out. The result shows that the applied method in this paper is an applicable technique and approximates the exact solution very well.