scholarly journals Analysis of the Generalized Inverse Polynomial Scheme to Initial Value Problems

2018 ◽  
Vol 3 (2) ◽  
Author(s):  
Olusola E Abolarin ◽  
Samuel W Akingbade
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Generalized Inverse ◽  
Series Method ◽  
Initial Value ◽  
Binomial Expansion ◽  
Problem Stability ◽  
Polynomial Scheme ◽  
Taylor’S Series

In this paper, we study the analysis of the generalized inverse polynomial scheme for the numerical solution of initial value problems of ordinary differential equation. At first, we generalize the scheme up to the fifth stage using the Binomial expansion and Taylor’s series method towards its derivation. The trend shows the generalization to the kth term. The analysis demonstrates the efficiency and the effectiveness of the generalized scheme.Keywords— Taylor’s Series, Initial Value Problem, Stability, Consistency, Convergence.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

scholarly journals Generalized (ψ,α,β)—Weak Contractions for Initial Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 266 ◽  
Author(s):  
Piyachat Borisut ◽  
Poom Kumam ◽  
Vishal Gupta ◽  
Naveen Mani
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Initial Value ◽  
Order Ordinary Differential Equation ◽  
Ordered Metric Spaces ◽  
First Order

A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

scholarly journals A Functionally-Fitted Block Numerov Method for Solving Second-Order Initial-Value Problems with Oscillatory Solutions

2021 ◽  
Vol 18 (6) ◽  
Author(s):  
R. I. Abdulganiy ◽  
Higinio Ramos ◽  
O. A. Akinfenwa ◽  
S. A. Okunuga
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Second Order ◽  
Initial Value ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Oscillatory Solutions ◽  
Type Method ◽  
Convergent Method

AbstractA functionally-fitted Numerov-type method is developed for the numerical solution of second-order initial-value problems with oscillatory solutions. The basis functions are considered among trigonometric and hyperbolic ones. The characteristics of the method are studied, particularly, it is shown that it has a third order of convergence for the general second-order ordinary differential equation, $$y''=f \left( x,y,y' \right) $$ y ′ ′ = f x , y , y ′ , it is a fourth order convergent method for the special second-order ordinary differential equation, $$y''=f \left( x,y\right) $$ y ′ ′ = f x , y . Comparison with other methods in the literature, even of higher order, shows the good performance of the proposed method.

scholarly journals A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
I. B. Aiguobasimwin ◽  
R. I. Okuonghae
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Initial Value ◽  
Large Interval ◽  
New Class ◽  
Second Derivatives ◽  
Stiff Odes ◽  
Runge Kutta ◽  
Special Case

In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered. The TDTSRK methods are a special case of multi-derivative Runge-Kutta methods proposed by Kastlunger and Wanner (1972). The methods considered herein incorporate only the first and second derivatives terms of ODEs. These methods possess large interval of stability when compared with other existing methods in the literature. The experiments have been performed on standard problems, and comparisons were made with some standard explicit Runge-Kutta methods in the literature.

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