Abstract and Applied Analysis

Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems

Abstract

We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method of the same stage. The intervals of absolute stability or periodicity of SIHM for ODE are also presented.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 136961, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511825

Digital Object Identifier
doi:10.1155/2013/136961

Mathematical Reviews number (MathSciNet)
MR3039174

Zentralblatt MATH identifier
1275.65042

Citation

Ahmad, S. Z.; Ismail, F.; Senu, N.; Suleiman, M. Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems. Abstr. Appl. Anal. 2013 (2013), Article ID 136961, 10 pages. doi:10.1155/2013/136961. https://projecteuclid.org/euclid.aaa/1393511825

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