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Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems
- Source :
- Abstract and Applied Analysis, Vol 2013 (2013)
- Publication Year :
- 2013
- Publisher :
- Hindawi Limited, 2013.
-
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.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 10853375 and 16870409
- Volume :
- 2013
- Database :
- Directory of Open Access Journals
- Journal :
- Abstract and Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.1c82697ba77140e182d25dfbaf8f375e
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2013/136961