A new numerical method is proposed for solving the delay ordinary differential equations (DODEs) under multiple time-varying delays or state-dependent delays. The finite difference scheme is used to approximate the ODEs, which together with the initial conditions constitute a system of nonlinear algebraic equations (NAEs). Then, a Fictitious Time Integration Method (FTIM) is used to solve these NAEs. Numerical examples confirm that the present approach is highly accurate and efficient with a fast convergence.
Cite This Article
C. Liu, "A fictitious time integration method for solving delay ordinary differential equations,"
Computers, Materials & Continua, vol. 10, no.1, pp. 97–116, 2009. https://doi.org/10.3970/cmc.2009.010.097