Numerical integration of partial differential equations using cubic splines

Abstract

This paper presents techniques for the numerical solution of partial differential equations using cubic spline collocation.

The main spline relations are presented and incorporated into solution procedures for partial differential equations. The computational algorithm in every case is a tridiagonal matrix system amenable to efficient inversion methods. Truncation errors and stability are briefly discussed. Finally, some examples of their application to parabolic and hyperbolic systems with mixed boundary conditions are presented.

The results obtained are encouraging and justify further research in this field.

Keywords:

• Cubic splines
• numerical integration of partial differential equations

C.R. Categories:

• 5.16
• 5.17