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2011•International journal of mathematics and computationRequires access

A Class Of Block Hybrid Adams Moulton Implicit Runge-Kutta (Bhamirk) Methods for Stiff Ordinary Differential Equations

Joshau P. Chollom, Geoffrey Micah Kumleng

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Abstract

This paper focuses on the reformulation of BHAM members previously constructed as Block Hybrid Adams Moulton Implicit Runge-kutta (BHAMIRK) methods in pursuance of the one step approach. These methods involve three-stages with collocation at previous mesh points and are shown to be A-stable,a stability requirement of multistep methods suitable for solving stiff Ordinary Differential Equations. Numerical results of experiments conducted using the BHAMIRK and BHAM members of the same step and order reveals a favorable comparison between them.

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What this paper is about

This paper focuses on the reformulation of BHAM members previously constructed as Block Hybrid Adams Moulton Implicit Runge-kutta (BHAMIRK) methods in pursuance of the one step approach. These methods involve three-stages with collocation at previous mesh points and are shown to be A-stable,a stability requirement of multistep methods suitable for solving stiff Ordinary Differential Equations. Numerical results of experiments conducted using the BHAMIRK and BHAM members of the same step and order reveals a favorable comparison between them.

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Available abstract

This paper focuses on the reformulation of BHAM members previously constructed as Block Hybrid Adams Moulton Implicit Runge-kutta (BHAMIRK) methods in pursuance of the one step approach. These methods involve three-stages with collocation at previous mesh points and are shown to be A-stable,a stability requirement of multistep methods suitable for solving stiff Ordinary Differential Equations. Numerical results of experiments conducted using the BHAMIRK and BHAM members of the same step and order reveals a favorable comparison between them.

Key concepts: Runge–Kutta methods, Mathematics, Linear multistep method, Numerical methods for ordinary differential equations, Ordinary differential equation, Collocation method, L-stability, Explicit and implicit methods

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