Stability of Runge–Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])
Copyright policy )Stability of Runge–Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])
This paper deals with the numerical solution of the delay differential equations with piecewise continuous arguments \(u'(t)=f(t, u(t), u(\alpha(t)))\). The stability of the Runge-Kutta methods is analyzed regarding stability regions. Conditions that the analytic stability region is contained in the numerical stability regions are obtained. Numerical results of the following problem \[ \begin{aligned} u_1'(t) & = -20u_1(t)-10.3 u_1([t]),\quad u_1(0)=1\\ u_2'(t) & = 10u_2(t)-10.001 u_2([t]),\quad u_2(0)=1 \end{aligned} \] are also given.
- Harbin Institute of Technology China (People's Republic of)
stability regions, asymptotic stability, Runge-Kutta methods, Asymptotic stability, Applied Mathematics, Piecewise continuous arguments, numerical results, Numerical approximation of solutions of functional-differential equations, piecewise continuous arguments, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Delay differential equation, Computational Mathematics, delay differential equation, Stability and convergence of numerical methods for ordinary differential equations
stability regions, asymptotic stability, Runge-Kutta methods, Asymptotic stability, Applied Mathematics, Piecewise continuous arguments, numerical results, Numerical approximation of solutions of functional-differential equations, piecewise continuous arguments, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Delay differential equation, Computational Mathematics, delay differential equation, Stability and convergence of numerical methods for ordinary differential equations
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