Solving delay differential equations using componentwise partitioning by Runge–Kutta method

摘要

Embedded singly diagonally implicit Runge–Kutta (SDIRK) method is used to solve stiff systems of delay differential equations (DDEs). 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.