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A Fourth Algebraic Order Explicit Trigonometrically- Fitted Modified Runge-Kutta Method for the Numerical Solution of Periodic IVPs
This study has constructed an explicit Trigonometrically-Fitted Modified Runge-Kutta (TFMRK) method for solving firstorder differential equations with periodic solutions. The newly developed method was made according to the method of Runge-Kutta Dorm and to fourth algebraic order. Numerical results for the new method were compared with the existing method, showing the potential of the new method over other existing methods.
Runge-Kutta Methods, Trigonometrically-Fitting and Periodic Solutions
- Simos TE. A family of fifth algebraic order trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrodinger equation. Comput Mater Sci.2005; 34:342–54.
- Simos TE, Aguiar JV. A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrodinger equation.Journal of Mathematical Chemistry. 2001; 30:121–31.
- Franco JM. Runge-Kutta methods adapted to the numerical integration of oscillatory problems. Numer Math Appl. 2004; 50:427–43.
- de Vyver HV. An embedded exponentially fitted RungeKutta-Nystom method for the numerical solution of orbital problems. New Astron. 2006; 11:577–87.
- Gautschi W. Numerical integration of ordinary differential equation based on trigonometrica polynomials. Numer Math. 1961; 3:381–97.
- Lyche T. Chebyshevian multistep methods for ordinary differential equation. Numer Math. 1972; 19:65–75.
- Aguiar JV, Simos TE. Review of multistep methods for the numerical solution of the radial Schrodinger equation. Int J Quant Chem. 2005; 103:278–90.
- Bettis DG. Runge-Kutta algorithms for oscillatory problems. Zeitschrift fur Angewandte Mathematik und Physik. 1979; 30:699–704.
- Paternoster B. Runge-Kutta (Nystrom) methods for ODEs with periodic solutions based on trigonometric polynomials. Applied Numerical Mathematics. 1998; 28:401–12.
- Berghe GV, De Meyer H, Daele MV, Van Hecke T.Exponentially fitted Runge-Kutta methods. Comput Phys Comm. 2000; 125:107–15.
- Berghe GV, De Meyer H, Van Daele M, Van Hecke T. Exponentially fitted explicit Runge-Kutta methods. Comput Phys Comm. 1999; 123:7–15.
- Zhang Y, Haitao, Fang Y, You X. A new trigonometrically fitted two derivative Runge-Kutta method for the numerical solution of the Schrodinger equation and related problems. Journal of Applied Mathematics. 2013; 937858:9.
- Fang Y, You X, Ming Q. Trigonometrically-fitted two derivative Runge-Kutta method for solving oscillatory differential equations. Numer Algor. 2014; 65:651–67.
- Butcher JC. Numerical Methods for Ordinary Differential Equations. Wiley & Sons LTD., England. 2008.
- Simos TE, Aguiar JV. A modi_ed Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrodinger equation and related problems. Comput Chem. 2001; 25:275–81.
- Sakas DP, Simos TE. A Fifth Order TrigonometricallyFitted Modified Runge-Kutta Zonneveld Method for the Numerical Solution of Orbital problems. Math Comp.2005; 42:903–20.
- Hairer E, Norsett SP, Wanner G. Solving Ordinary Differential Equations I, Nonstiff Problems. Springer, Berlin. 1993.
- Chawla MM, Rao PS. High-accuracy P-stable methods for IMA Journal of Numerical Analysis. 1985; 5:21–220.
- van der Houwen PJ, Sommeijer BP. Explicit Runge-Kutta (-Nystrom) methods with reduced phase errors for computing oscillating solutions. SIAM Journal on Numerical Analysis. 1987; 24(3):595–617.
- Stiefel E, Bettis DG. Stabilization of Cowell’s methods.Numer Math. 1969; 13:154–75.
- Moo KW, Senu N, Ismail F, Suleiman M. New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nystrom methods for oscillatory problems. Abstract and Applied Analysis. 2013; 939367:9.
- Allen RC Jr, Wing GM. An invariant imbedding algorithm for the solution of inhomogeneous linear two-point boundary value problems. J Computer Physics. 1974; 14:40–58.
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