A New Integrator of Runge-Kutta Type for Directly Solving General Third-order ODEs with Application to Thin Film Flow Problem

2018 ◽  
Vol 12 (4) ◽  
pp. 775-784
Author(s):  
F. A. Fawzi ◽  
N. Senu ◽  
F. Ismail ◽  
Z. A. Majid
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Flow Problem ◽  
Thin Film Flow ◽  
Third Order ◽  
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.

scholarly journals Adaptive Polynomial Method for Solving Third Order ODE with Application in Thin Film Flow

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Mohammad T. Haweel ◽  
O. Zahran ◽  
Fathi E. Abd El-Samie
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Polynomial Method ◽  
Thin Film Flow ◽  
Third Order
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