A third order Runge-Kutta method based on a linear combination of arithmetic mean, geometric mean and centroidal mean for first order differential equation

2020 ◽  
Author(s):  
R. Gethsi Sharmila ◽  
S. Suvitha ◽  
M. Sarah Sunithy
Keyword(s):  
Differential Equation ◽  
Linear Combination ◽  
Order Differential Equation ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Kutta Method ◽  
Third Order ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta

MULTIDERIVATIVE HYBRID IMPLICIT RUNGE-KUTTA METHOD FOR SOLVING STIFF SYSTEM OF A FIRST ORDER DIFFERENTIAL EQUATION

2018 ◽  
Vol 106 (2) ◽  
pp. 543-562
Author(s):  
Olusheye A. Akinfenwa ◽  
Solomon A. Okunuga ◽  
Blessing I. Akinnukawe ◽  
Uthman O. Rufai ◽  
Ridwanulahi I. Abdulganiy
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Kutta Method ◽  
Stiff System ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Mechee ◽  
N. Senu ◽  
F. Ismail ◽  
B. Nikouravan ◽  
Z. Siri
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Film Flow ◽  
New Method ◽  
Kutta Method ◽  
Thin Film Flow ◽  
Third Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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