MOMOH ADELEGAN LUKUMAN
Publication
Publisher:
Inderscience Publishers (IEL)
Publication Type:
Journal
Publication Title:
Insight Into 2-step Continuous Block Method For Solving Mixture Model And SIR Model
Publication Authors:
M.K. Duromola*, A.L. Momoh, M.A. Rufai And I.L. Animasaun
Year Published:
2021
Abstract:
Understanding of the solutions of first-order ordinary differential
equations (ODEs), mixture model and SIR model in order to develop deep insight
and exploration are major problems before the experts, biologists, scientists, and
mathematicians. In all these problems, the governing equations are either single
first-order or coupled ODEs kind of initial value problem (IVP). In this paper, a
polynomial function q(x) that passes through the points (xn, yn), (xn+1, yn+1),
. . . , (xn+2, yn+2) was adopted as the basis function that leads to third derivatives
continuous 2-step block method suitable to solve first order initial value problems
of ODEs. Upon using the newly proposed scheme to solve linear ODEs (i.e.,
mixture theory) and nonlinear ODE (i.e., SIR model), it is worth concluding that
the algorithm is not only efficient but minimises error
Publisher:
American Journal Of Computational Mathematics
Publication Type:
Journal
Publication Title:
Hybrid Numerical Method With Block Extension For Direct Solution Of Third Order Ordinary Differential Equations
Publication Authors:
Duromola M. K. And Momoh A. L.
Year Published:
2019
Abstract:
This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order
ordinary differential equations. Power series was used as the basis function
for the solution of the IVP. An approximate solution from the basis function
was interpolated at some selected off-grid points while the third derivative of
the approximate solution was collocated at all grid and off-grid points to
generate a system of linear equations for the determination of the unknown
parameters. The derived method was tested for consistency, zero stability,
convergence and absolute stability. The method was implemented with five
test problems including the Genesio equation to confirm its accuracy and
usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the
results with some existing methods shows the superiority of the accuracy of
the method
