IJPAM: Volume 120, No. 1 (2018)

Title

AN EFFICIENT OF DIRECT INTEGRATOR OF
RUNGE-KUTTA TYPE METHOD FOR SOLVING
$y'''=f(x,y,y')$ WITH APPLICATION TO THIN
FILM FLOW PROBLEM

Authors

Firas Adel Fawzi$^1$, Norazak Senu$^2$, Fudziah Ismail$^2$
and Zanariah Abd. Majid$^2$
$^1$Department of Mathematics
Faculty of Computer Science and Mathematics
Tikrit University, Sallah AL-Deen, IRAQ
$^2$Institute for Mathematical Research
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA

Abstract

In this paper, we proposed a fifth-order Runge-Kutta (RK) technique for regulating coordination about third-order ordinary differential equations (ODEs) of the structure $y'''=f(x,y,y')$ indicated similarly as RKTG method is constructed. The order state about RKTG method up to order six were proved and verified. In view of those order conditions developed, four-stage fifth-order express Runge-Kutta methods of techniques were constructed. The zero Strength of the new system was indicated. The Different types for third-order ODEs need been derived utilizing the new system and also some numerical comparison were conducted when the same issue will be decreased of the first-order framework of equations which are solved using existing Runge-Kutta techniques. The numerical investigation of a third-order tribute on thin film flow for viscous liquid in applied mathematical physics. Numerical outcomes indicated that those new proposed method is more efficient in terms of accuracy and number of function evaluations of capacity assessments.

History

Received: May 15, 2017
Revised: June 19, 2018
Published: August 13, 2018

AMS Classification, Key Words

AMS Subject Classification: 65L05, 65L06
Key Words and Phrases: Runge-Kutta type methods, general third-order ODEs, order conditions, thin film flow

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How to Cite?

DOI: 10.12732/ijpam.v120i1.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 1
Pages: 27 - 50


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