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 is 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 Adams- Moulton methods respectively.
Singh, Gurjinder; Kanwar, V.; and Bhatia, Saurabh
Exponentially Fitted Variants of the Two-Step Adams-Bashforth Method for the Numerical Integration of Initial Problems,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
2, Article 26.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss2/26