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2014•Unpublished venueRequires access

A Three Step Implicit Hybrid Linear Multistep Method for the Solution of Third Order Ordinary Differential Equations

Umaru Mohammed

Open publisher page 13 citations

Abstract

A Linear Multistep Hybrid Method (LMHM) with contin uous coefficients is considered and directly applied to solve third orde r Initial Value Problems (IVPs). The continuous method is used to obtain Mul tiple Finite Difference Methods (MFDMs) each of order 5 which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block meth od and verifying that the block method is zero-stable and consistent. The sup eriority of the MFDMs over the existing methods is established numerically.

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What this paper is about

A Linear Multistep Hybrid Method (LMHM) with contin uous coefficients is considered and directly applied to solve third orde r Initial Value Problems (IVPs). The continuous method is used to obtain Mul tiple Finite Difference Methods (MFDMs) each of order 5 which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block meth od and verifying that the block method is zero-stable and consistent. The sup eriority of the MFDMs over the existing methods is established numerically.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A Linear Multistep Hybrid Method (LMHM) with contin uous coefficients is considered and directly applied to solve third orde r Initial Value Problems (IVPs). The continuous method is used to obtain Mul tiple Finite Difference Methods (MFDMs) each of order 5 which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block meth od and verifying that the block method is zero-stable and consistent. The sup eriority of the MFDMs over the existing methods is established numerically.

Key concepts: Linear multistep method, Ordinary differential equation, Initial value problem, Convergence (economics), Applied mathematics, Numerical methods for ordinary differential equations, Mathematics, Block (permutation group theory)

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