Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method
From MaRDI portal
Publication:1065507
DOI10.1007/BF01389713zbMath0577.65064OpenAlexW2073816666MaRDI QIDQ1065507
Marino Zennaro, Alfredo Bellen
Publication date: 1985
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/133035
implicit Runge-Kutta methoddelay differential equationscollocationcomparisonspredictor-correctorstep-size controlNumerical tests
Numerical methods for initial value problems involving ordinary differential equations (65L05) General theory of functional-differential equations (34K05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)
Related Items
Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations, A mixed finite element for the Stokes problem using quadrilateral elements, Issues in the numerical solution of evolutionary delay differential equations, Numerical solution of piecewise constant delay systems based on a hybrid framework, A Legendre-Gauss-Radau spectral collocation method for first order nonlinear delay differential equations, Ana priorierror analysis of thehp-version of theC0-continuous Petrov-Galerkin method for nonlinear second-order delay differential equations, Errors of linear multistep methods and Runge-Kutta methods for singular perturbation problems with delays., On the solutions of a system of linear retarded and advanced differential equations by the Bessel collocation approximation, Numerical computation of derivatives in systems of delay differential equations, The numerical solution of neutral functional differential equations by Adams predictor-corrector methods, The tracking of derivative discontinuities in systems of delay- differential equations, DELSOL -- a numerical code for the solution of systems of delay- differential equations, An \(h\)-\(p\) version of the continuous Petrov-Galerkin method for nonlinear delay differential equations, Analysis of linear piecewise constant delay systems using a hybrid numerical scheme, Error control for initial value problems with discontinuities and delays, The tolerance proportionality of adaptive ODE solvers, The use of polynomial spline functions for the solution of system of second order delay differential equations, An \(hp\)-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays, Some applications of continuous Runge-Kutta methods, An \(h\)-\(p\) version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations, Error of one-leg methods for singular perturbation problems with delays, Retarded differential equations, Legendre-Gauss-Lobatto spectral collocation method for nonlinear delay differential equations, Spline approximation for first Order fredholm delay integro-differential equations, Computer solutions of state-dependent delay differential equations
Cites Work
- Unnamed Item
- Unnamed Item
- One-step collocation for delay differential equations
- Numerical solution of retarded initial value problems: Local and global error and stepsize control
- Numerical treatment of delay differential equations by Hermite interpolation
- On the computational solution of a class of functional differential equations
- The real-pole sandwich for rational approximations and oscillation equations
- One-Step Collocation: Uniform Superconvergence, Predictor-Corrector Method, Local Error Estimate
- Algorithm 497: Automatic Integration of Functional Differential Equations [D2]
- Automatic Integration of Functional Differential Equations: An Approach
- One-Step Piecewise Polynomial Galerkin Methods for Initial Value Problems