Solving delay differential equations using componentwise partitioning by Runge-Kutta method. (English) Zbl 1024.65057
Summary: Embedded singly diagonally implicit Runge-Kutta method is used to solve stiff systems of delay differential equations. The delay argument is approximated using Hermite interpolation. Initially the whole system is considered as nonstiff and solved using simple iteration. When stiffness is indicated, the appropriate equation is placed into the stiff subsystem and solved using Newton iteration. This type of partitioning is called componentwise partitioning. The process is continued until all the equations have been placed in the right subsystem. Numerical results based on componentwise partitioning and intervalwise partitioning are tabulated and compared.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |
Keywords:
comparison of methods; singly diagonally implicit Runge-Kutta method; stiff delay differential equations; componentwise partitioning; numerical resultsReferences:
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