FOURTH ORDER 4-STAGES IMPROVED RUNGE-KUTTA METHOD WITH MINIMIZED ERROR NORM.
- Resource Type
- Article
- Authors
- Rabiei, Faranak; Ismail, Fudziah
- Source
- AIP Conference Proceedings. 2014, Vol. 1613, p153-158. 6p. 3 Charts, 1 Graph.
- Subject
- *RUNGE-Kutta formulas
*ORDINARY differential equations
*COEFFICIENTS (Statistics)
*SUBSTITUTIONS (Mathematics)
*INITIAL value problems
*POLYNOMIALS
- Language
- ISSN
- 0094-243X
In this paper the improved Runge-Kutta method of order four with 4-stages for solving first order ordinary differential equation is proposed. The method is based on classical Runge-Kutta (RK) method also can be considered as special class of two-step method. Here, the coefficients of the method are obtained using the minimization of the error norm up to order five. The improved method with only 4-stages is more accurate than fourth order 4-stages RK method. Therefore it is computationally more efficient than the existing RK method. A number of test problems are solved and the numerical results compared with the existing RK method are given. [ABSTRACT FROM AUTHOR]