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A Computational Study of the Boundary Value Methods and the Block Unification Methods for

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  • T. A. Biala

Abstract

We derive a new class of linear multistep methods (LMMs) via the interpolation and collocation technique. We discuss the use of these methods as boundary value methods and block unification methods for the numerical approximation of the general second-order initial and boundary value problems. The convergence of these families of methods is also established. Several test problems are given to show a computational comparison of these methods in terms of accuracy and the computational efficiency.

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  • T. A. Biala, 2016. "A Computational Study of the Boundary Value Methods and the Block Unification Methods for," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-14, April.
    • Handle: RePEc:hin:jnlaaa:8465103
    DOI: 10.1155/2016/8465103
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    Cited by:

    1. Modebei, Mark I. & Adeniyi, Rapheal B. & Jator, Samuel N. & Ramos, Higinio, 2019. "A block hybrid integrator for numerically solving fourth-order Initial Value Problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 680-694.
    2. Ramos, Higinio & Singh, Gurjinder, 2022. "Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator," Applied Mathematics and Computation, Elsevier, vol. 421(C).

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