Non-polynomial cubic spline methods for the solution of parabolic equations

Abstract

Second-order parabolic partial differential equations are solved by using a new three level method based on non-polynomial cubic spline in the space direction and finite difference in the time direction. Stability analysis of the method has been carried out and we have shown that our method is unconditionally stable. It has been shown that by suitably choosing the parameters most of the previous known methods for homogeneous and non-homogeneous cases can be obtained from our method. We also obtain a new high accuracy scheme of O(k ⁴+h ⁴). Numerical examples are given to illustrate the applicability and efficiency of the new method.

Keywords:

• Second-order parabolic equation
• Non-polynomial cubic spline
• Unconditionally stable
• Finite difference scheme

CCS Category :

• G.1.8