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 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 On the boundedness of solution of the second order ordinary differential equation with damping term and involution

2021 ◽  
Vol 102 (2) ◽  
pp. 16-24
Author(s):  
A. Ashyralyev ◽  
◽  
M. Ashyralyyeva ◽  
O. Batyrova ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Second Order ◽  
Stability Estimates ◽  
Damping Term ◽  
Initial Value ◽  
Order Ordinary Differential Equation ◽  
Linear Differential

In the present paper the initial value problem for the second order ordinary differential equation with damping term and involution is investigated. We obtain equivalent initial value problem for the fourth order ordinary differential equations to the initial value problem for second order linear differential equations with damping term and involution. Theorem on stability estimates for the solution of the initial value problem for the second order ordinary linear differential equation with damping term and involution is proved. Theorem on existence and uniqueness of bounded solution of initial value problem for second order ordinary nonlinear differential equation with damping term and involution is established.

scholarly journals On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

1982 ◽  
Vol 37 (8) ◽  
pp. 830-839 ◽  
Author(s):  
A. Salat
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Infinite Sequence ◽  
Periodic Coefficient ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Magnetic Surfaces ◽  
Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

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.

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

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