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2013•Applications and Applied Mathematics: An International Journal (AAM)Requires access

Exponentially Fitted Variants of the Two-Step Adams-Bashforth Method for the Numerical Integration of Initial Value Problems

Gurjinder Singh, V. Kanwar, Saurabh Bhatia

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Abstract

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants are discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step AdamsMoulton methods respectively.

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What this paper is about

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants are discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step AdamsMoulton methods respectively.

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Available abstract

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants are discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step AdamsMoulton methods respectively.

Key concepts: Linear multistep method, Ode, Numerical methods for ordinary differential equations, Mathematics, Ordinary differential equation, Applied mathematics, Backward differentiation formula, Numerical integration

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