# Hybrid Block Methods with Constructed Orthogonal Basis for Solution of Third-Order Ordinary Differential Equations

## Authors

• Folake Lois Joseph Department of Mathematical Sciences, Bingham University Karu,Nigeria
• Adeyemi Sunday Olagunju Department of Mathematics, Federal University of Lafia, Nigeria
• Emmanuel Oluseye Adeyefa Department of Mathematics, Federal University Oye-Ekiti, Nigeria
• Adewale Adeyemi James Mathematics Division, American University of Nigeria, Yola, Nigeria

## Keywords:

Hybrid block, Collocation, Interpolation, Third-order ODE, Integration scheme

## Abstract

In this work, an orthogonal polynomial with weight function w(x) =x2 + x + 1 in the interval [-1, 1] was constructed and used as the basis function to develop block methods, using collocation and interpolation approach. An efficient class of continuous and discrete numerical integration schemes of implicit hybrid form for third-order problems were developed and successfully implemented. Three different problems were solved with these schemes and they performed favourably. The investigation, using the appropriate existing theorems, shows that the methods are consistent, zero-stable and hence, convergent.

Dimensions

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2022-12-22

## How to Cite

Hybrid Block Methods with Constructed Orthogonal Basis for Solution of Third-Order Ordinary Differential Equations. (2022). Journal of the Nigerian Society of Physical Sciences, 5(1), 865. https://doi.org/10.46481/jnsps.2023.865

## Section

Original Research

## How to Cite

Hybrid Block Methods with Constructed Orthogonal Basis for Solution of Third-Order Ordinary Differential Equations. (2022). Journal of the Nigerian Society of Physical Sciences, 5(1), 865. https://doi.org/10.46481/jnsps.2023.865