Stabilized fourth order extended methods for the numerical solution of odes

Abstract

Recently, Kondrat and Jacques [1] gave an extended two-step fourth order A-stable method; the reason noted for giving a two-step method is that a one-step method of the type is not possible.

Firstly, we show that it is possible to obtain a two-parameter family of such methods which are one-step, fourth order and A-stable; and, there exists a one-parameter sub-family of these methods which are, in addition, L-stable. Secondly, from among the extended two-step methods, it is natural to ask if the well-known Simpson's rule can be stabilized; we present an A-stabilized version of Simpson's rule.

Keywords:

• Initial-value problem
• ordinary differential equations
• linear multistep methods
• extended methods
• one-step
• two-step
• A-stability
• L-stability
• Simpson's rule

C.R Categories:

• G.1.7