Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems
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 fif...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2013
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/30209/1/30209.pdf http://psasir.upm.edu.my/id/eprint/30209/ https://www.hindawi.com/journals/aaa/2013/136961/abs/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|