New Generalized Algorithm for Developing k-Step Higher Derivative Block Methods for Solving Higher Order Ordinary Differential Equations

Adeyeye, Oluwaseun; Omar, Zurni

doi:10.5614/j.math.fund.sci.2018.50.1.4

Cited by 4 publications

(1 citation statement)

References 13 publications

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“…These k values were selected in order to obtain suitable block methods of equal or lower order to the other previously developed numerical methods for comparison. Following the linear block approach by [25], the unknown coefficients for the 1 k  block method are derived from the expression 1 ,…”

Section: Methodsmentioning

confidence: 99%

Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model

Adeyeye¹,

Omar²

2021

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Some of the issues relating to the human immunodeficiency virus (HIV) epidemic can be expressed as a system of nonlinear first order ordinary differential equations. This includes modelling the spread of the HIV virus in infecting CD4+T cells that help the human immune system to fight diseases. However, real life differential equation models usually fail to have an exact solution, which is also the case with the nonlinear model considered in this article. Thus, an approximate method, known as the block method, is developed to solve the system of first order nonlinear differential equation. To develop the block method, a linear block approach was adopted, and the basic properties required to classify the method as convergent were investigated. The block method was found to be convergent, which ascertained its usability for the solution of the model. The solution obtained from the newly developed method in this article was compared to previous methods that have been adopted to solve same model. In order to have a justifiable basis of comparison, two-step length values were substituted to obtain a one-step and two-step block method. The results show the newly developed block method obtaining accurate results in comparison to previous studies. Hence, this article has introduced a new method suitable for the direct solution of first order differential equation models without the need to simplify to a system of linear algebraic equations. Likewise, its convergent properties and accuracy also give the block method an edge over existing methods.

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Section: Methodsmentioning

confidence: 99%

Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model

Adeyeye¹,

Omar²

2021

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show abstract

Investigation of a hyperbolic annular fin with temperature dependent thermal conductivity by two step third derivative block method (TSTDBM)

et al. 2020

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Estimating server utilization rate in single server queuing models using an approximate solution of stiff fluid flow model

Mueen

2020

Ain Shams Engineering Journal

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New Generalized Algorithm for Developing k-Step Higher Derivative Block Methods for Solving Higher Order Ordinary Differential Equations

Cited by 4 publications

References 13 publications

Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model

Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model

Investigation of a hyperbolic annular fin with temperature dependent thermal conductivity by two step third derivative block method (TSTDBM)

Estimating server utilization rate in single server queuing models using an approximate solution of stiff fluid flow model

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