A Linearly Fourth Order Multirate Runge–Kutta Method with Error Control

2015 ◽  
Vol 66 (1) ◽  
pp. 177-195 ◽  
Author(s):  
Pak-Wing Fok
Keyword(s):  
Fourth Order ◽  
Error Control ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

Elastohydrodynamic Lubrication in Rolling and Sliding Contacts

1972 ◽  
Vol 94 (4) ◽  
pp. 324-329 ◽  
Author(s):  
C. M. Rodkiewicz ◽  
V. Srinivasan
Keyword(s):  
Film Thickness ◽  
Quadrature Formula ◽  
Fourth Order ◽  
Elastohydrodynamic Lubrication ◽  
Experimental Film ◽  
Kutta Method ◽  
Sliding Contacts ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Good Agreement

A solution to the elastohydrodynamic lubrication problem for the case of two rolling cylinders, at different speeds, is presented. The lubricant is assumed compressible throughout the region. The fourth-order Runge-Kutta method for the lubricant and an improved quadrature formula for the elastic calculations are used. Pressure and film-thickness profiles are presented for different rolling velocities. There is a good agreement with the experimental film thickness data, available in literature.

scholarly journals Fuzzy version of a developed fourth order Runge Kutta method for solving differential equations with fuzzy initial values

2016 ◽  
Author(s):  
Amirah Ramli ◽  
Rokiah @ Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Abdul Razak Salleh
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Kutta Method ◽  
Initial Values ◽  
Runge Kutta Method ◽  
Runge Kutta
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