ScholarLens Back to search
2014•American journal of mathematics and statisticsOpen access

A Family of Block Methods Derived from TOM and BDF Pairs for Stiff Ordinary Differential Equations

I. J. Ajie, M. N. O. Ikhile, P. Onumanyi

Open full text 0 citations

Abstract

In this paper, we introduced a family of self-starting L(α)-stable linear multistep block methods (LMBMs) for solving stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The block methods are constructed by pairing k-step Top Order Methods (TOMs) and 2k-step Backward Differentiation Formulas (BDF) and shifting them (2k - 2) times as in Ajie et al (2014). The methods are of order 2k and their performance on the numerical examples considered shows that their accuracies increase as the order increases. Keywords Top Order Method (TOM), Backward Differentiation Formulas (BDF), L(α)-stable, A(α)-stable, Linear Multistep Block Methods (LMBMs)

About this research paper

What this paper is about

In this paper, we introduced a family of self-starting L(α)-stable linear multistep block methods (LMBMs) for solving stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The block methods are constructed by pairing k-step Top Order Methods (TOMs) and 2k-step Backward Differentiation Formulas (BDF) and shifting them (2k - 2) times as in Ajie et al (2014). The methods are of order 2k and their performance on the numerical examples considered shows that their accuracies increase as the order increases. Keywords Top Order Method (TOM), Backward Differentiation Formulas (BDF), L(α)-stable, A(α)-stable, Linear Multistep Block Methods (LMBMs)

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, we introduced a family of self-starting L(α)-stable linear multistep block methods (LMBMs) for solving stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The block methods are constructed by pairing k-step Top Order Methods (TOMs) and 2k-step Backward Differentiation Formulas (BDF) and shifting them (2k - 2) times as in Ajie et al (2014). The methods are of order 2k and their performance on the numerical examples considered shows that their accuracies increase as the order increases. Keywords Top Order Method (TOM), Backward Differentiation Formulas (BDF), L(α)-stable, A(α)-stable, Linear Multistep Block Methods (LMBMs)

Key concepts: Mathematics, Linear multistep method, Ordinary differential equation, Backward differentiation formula, Ode, Block (permutation group theory), Applied mathematics, Initial value problem

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A Family of Block Methods Derived from TOM and BDF Pairs for Stiff Ordinary Differential Equations — Research Paper | ScholarLens