On the asymptotic behaviour of solutions of certain fifth-order ordinary differential equations

2003 ◽  
Vol 24 (8) ◽  
pp. 893-901 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Ordinary Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Fifth Order

scholarly journals Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation

Algorithms ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 10 ◽  
Author(s):  
Nizam Ghawadri ◽  
Norazak Senu ◽  
Firas Adel Fawzi ◽  
Fudziah Ismail ◽  
Zarina Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Foundation ◽  
Fourth Order ◽  
Sixth Order ◽  
Test Problems ◽  
Type Method ◽  
Ill Posed ◽  
Runge Kutta ◽  
Fifth Order

In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods.

scholarly journals On Asymptotic Behaviour of Solutions ton-Dimensional Systems of Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
H. Šamajová ◽  
E. Špániková
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Functional Differential Systems ◽  
Functional Differential

This paper presents the properties and behaviour of solutions to a class ofn-dimensional functional differential systems of neutral type. Sufficient conditions for solutions to be either oscillatory, orlimt→∞yi(t)= 0, orlimt→∞|yi(t)|=∞,i=1,2,…,n, are established. One example is given.

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