Stability of Runge–Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])+a1u([t−1])
Copyright policy )Stability of Runge–Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])+a1u([t−1])
The authors discuss the numerical solution of the initial value problem \(u'(t) = a u(t) + a_0 u([t]) + a_1 u([t-1])\), \(u(0) = u_0\), \(u(-1) = u_{-1}\), where \([\cdot]\) denotes the floor function (round down to nearest integer). This is a special case of a delay differential equation with piecewise continuous argument. The numerical methods under consideration are of Runge-Kutta type. The authors first explain how standard Runge-Kutta methods can be applied to this class of problems. Then, the asymptotic stability of various special types of Runge-Kutta methods (e.g., Gauss, Lobatto, and Radau) is investigated.
- Harbin Institute of Technology China (People's Republic of)
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Numerical solution of boundary value problems involving ordinary differential equations, asymptotic stability, delay differential equation, piecewise continuous argument, Runge-Kutta method, Numerical approximation of solutions of functional-differential equations, Stability and convergence of numerical methods for ordinary differential equations
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Numerical solution of boundary value problems involving ordinary differential equations, asymptotic stability, delay differential equation, piecewise continuous argument, Runge-Kutta method, Numerical approximation of solutions of functional-differential equations, Stability and convergence of numerical methods for ordinary differential equations
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