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Improved Extended Runge-Kutta-like Method for Solving First Order IVPs.
In this research, we proposed a family of improved extended Runge-Kutta-like methods which incorporate the function as well as the derivative of the function for the numerical integration of autonomous and non-autonomous ordinary differential equations. The proposed methods are more accurate than the existing methods in the literature and acquire bigger regions of stability. Numerical examples illustrating the computational accuracy are presented and the stability regions are also shown.
Absolute Error, Absolute Stability, Extended Runge-Kutta, Ordinary Differential Equations.
- Butcher JC. The numerical analysis of ordinary differential equations, Runge–Kutta and General Linear Methods.Wiley, New York; 1987.
- Domand JR. Numerical methods for differential equations: A computational approach. CRC Press, New York; 1996.
- Goeken D, Johnson O. Runge-Kutta with higher order derivative approximations. Applied Numerical Mathematics.2000; 34:207–18.
- Xinyuan W. A class of Runge-Kutta formulae of order three and four with reduced evaluations of function. Applied Mathematics and Computation. 2003; 146:417–32.
- Phohomsiri P, Udwadia FE. Acceleration of Runge-Kutta integeration schemes, Discrit. Dynamic. Nature Society.2004; 2:307–14.
- Xinyuan W, Jianlin X. Extended Runge-Kutta-like formulae.Applied Numerical Mathematics. 2006:1584–605.
- Udwadia FE, Farahani A. Accelerated Runge-Kutta methods, Discrete Dynamics in Nature and Society. 2008. DOI: 10.1155/2008/790619.
- Rabiei F, Ismail F. Fifth-order Improved Runge-Kutta method for solving ordinary differential equation.Proceeding of WSEAS Conference, Penang, Malaysia; 2011.p. 129–33.
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