Implicit Seven Step Simpson’s Hybrid Block Second-derivative Method with One Off-Step Point for Solving Second Order Ordinary Differential Equations

A. H. Umaru, J. Z. Donald and Y. Skwame
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A. H. Umaru: Department Of Mathematics, Adamawa State University Mubi Nigeria
J. Z. Donald: Department Of Mathematics, Adamawa State University Mubi Nigeria
Y. Skwame: Department Of Mathematics, Adamawa State University Mubi Nigeria

International Journal of Research and Innovation in Applied Science, 2022, vol. 7, issue 9, 07-11

Abstract: This paper is concerned with the construction of continuous Seven-Step implicit hybrid block Simpson’s Second derivative method for solving initial value problems of second order ordinary differential equations were derived through interpolation and collocation method using maple software. Power series approximation method was used to generate the unknown parameters in the corrector. These Continuous formulations were evaluated at some desired points to give the discrete schemes which constitute the hybrid block method. The constructed block method is consistent, zero-stable and A(α)-Stable. Numerical results obtained using the new block method show that it superior on some system of initial value problems. The study revealed that our new method performed better.

Date: 2022
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