Numerical stability, resolvent conditions and delay differential equations

DOI10.1016/S0168-9274(97)00023-8zbMath0880.65064MaRDI QIDQ1360546

Marc N. Spijker

Publication date: 2 February 1998

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilitydelay differential equationsKreiss resolvent conditionerror growth analysis

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) General theory of functional-differential equations (34K05) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

Compact \(\theta \)-method for the generalized delay diffusion equation ⋮ The stability of Radau IIA collocation processes for delay differential equations ⋮ Asymptotic stability analysis of the linear θ-method for linear parabolic differential equations with delay ⋮ The sharpness of stability estimates corresponding to a general resolvent condition ⋮ Resolvent conditions and bounds on the powers of matrices, with relevance to numerical stability of initial value problems

Cites Work

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• On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods
• On resolvent conditions and stability estimates
• P-stability properties of Runge-Kutta methods for delay differential equations
• On the asymptotic stability of \(\theta\)-methods for delay differential equations
• Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem
• The equivalence of \(L^ q-\)stability, the resolvent condition, and strict H-stability
• On a conjecture by LeVeque and Trefethen related to the Kreiss matrix theorem
• Two counterexamples related to the Kreiss matrix theorem
• Stability estimates for families of matrices of nonuniformly bounded order
• On the resolvent condition in the Kreiss matrix theorem
• The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
• The Stability of Difference Formulas for Delay Differential Equations
• Über Die Stabilitätsdefinition Für Differenzengleichungen Die Partielle Differentialgleichungen Approximieren
• Special stability problems for functional differential equations
• From the Buffon Needle Problem to the Kreiss Matrix Theorem
• Stability of Rational Multistep Approximations of Holomorphic Semigroups
• On a matrix theorem due to H. O. Kreiss

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