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

Folake Lois  Joseph; Adeyemi Sunday Olagunju; Emmanuel Oluseye Adeyefa; Adewale Adeyemi James

doi:10.46481/jnsps.2023.865

Authors

Folake Lois Joseph
Department of Mathematical Sciences, Bingham University Karu,Nigeria
https://orcid.org/0000-0003-1312-163X
Adeyemi Sunday Olagunju
[email protected]

Department of Mathematics, Federal University of Lafia, Nigeria
Emmanuel Oluseye Adeyefa
Department of Mathematics, Federal University Oye-Ekiti, Nigeria
https://orcid.org/0000-0003-0942-6430
Adewale Adeyemi James
Mathematics Division, American University of Nigeria, Yola, Nigeria
https://orcid.org/0000-0003-2257-5596

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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