TY - JOUR

T1 - Stability analysis of two-step Runge-Kutta methods for delay differential equations

AU - Bartoszewski, Z.

AU - Jackiewicz, Zdzislaw

N1 - Funding Information:
The authors wish to express their gratitude to anonymous referees for their helpful remarks. *The work of this author was partially supported by the National Science Foundation under Grant NSF DMS-9971164.

PY - 2002/7

Y1 - 2002/7

N2 - We investigate stability properties of two-step Runge-Kutta methods with respect to the linear test equation y′(t) = ay(t) + by (t - ρ), t ≥ 0, y(t) = g(t), t ∈ [-ρ,0], where a and b are complex parameters. It is known that the solution y(t) to this equation tends to zero at t → ∞ if |b| < - Re(a). We will show that under some conditions this property is inherited by any A-stable two-step Runge-Kutta method applied on a constrained mesh to delay differential equations, i.e., that the corresponding method is P-stable.

AB - We investigate stability properties of two-step Runge-Kutta methods with respect to the linear test equation y′(t) = ay(t) + by (t - ρ), t ≥ 0, y(t) = g(t), t ∈ [-ρ,0], where a and b are complex parameters. It is known that the solution y(t) to this equation tends to zero at t → ∞ if |b| < - Re(a). We will show that under some conditions this property is inherited by any A-stable two-step Runge-Kutta method applied on a constrained mesh to delay differential equations, i.e., that the corresponding method is P-stable.

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U2 - 10.1016/S0898-1221(02)00131-1

DO - 10.1016/S0898-1221(02)00131-1

M3 - Article

AN - SCOPUS:0036630251

VL - 44

SP - 83

EP - 93

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 1-2

ER -