On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods

DOI10.1007/BF01937328zbMath0506.65030OpenAlexW1988537789MaRDI QIDQ1836968

Michel Crouzeix, Marc N. Spijker, Willem H. Hundsdorfer

Publication date: 1983

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01937328

zbMATH Keywords

systems of algebraic equationsimplicit Runge-Kutta methodsunique solutions23, 84-91 (1983)

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (31)

Suitability of Runge-Kutta methods ⋮ The order of B-convergence of algebraically stable Runge-Kutta methods ⋮ On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations ⋮ The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations ⋮ On the solvability of the systems of equations arising in implicit Runge- Kutta methods ⋮ Stage-based interpolation Runge-Kutta methods for nonlinear Volterra functional differential equations ⋮ The dichotomy of stiffness: Pragmatism versus theory ⋮ Algebraic stability and error propagation in Runge-Kutta methods ⋮ Error bounding functions for Runge-Kutta methods ⋮ On the D-suitability of implicit Runge-Kutta methods ⋮ The existence and uniqueness of solutions for the nonlinear algebraic equations in implicit r-k methods ⋮ The existence and uniqueness of solutions for the nonlinear algebraic equations in implicit R-K methods ⋮ Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems ⋮ Stability and B-convergence of general linear methods ⋮ On the relation between algebraic stability and B-convergence for Runge- Kutta methods ⋮ On the unique solvability of the Runge-Kutta equations ⋮ On the existence of solution of stage equations in implicit Runge-Kutta methods ⋮ Strong contractivity properties of numerical methods for ordinary and delay differential equations ⋮ Analysis of fully discrete approximations for dissipative systems and application to time-dependent nonlocal diffusion problems ⋮ On conditions for the existence and uniqueness of solutions to the algebraic equations in Runge-Kutta methods ⋮ Unique solvability of nonlinear systems arising in the multiderivative block methods ⋮ Runge-Kutta methods: Some historical notes ⋮ An algebraic characterization of B-convergent Runge-Kutta methods ⋮ Error bounds for the solution to the algebraic equations in Runge-Kutta methods ⋮ Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods ⋮ On the use of parallel processors for implicit Runge-Kutta methods ⋮ Feasibility and contractivity in implicit Runge-Kutta methods ⋮ A necessary condition for BSI-stability ⋮ Convergence results for general linear methods on singular perturbation problems ⋮ Algebraic stability and the existence of solutions of implicit Runge- Kutta equations ⋮ Reducible Runge-Kutta methods

Cites Work

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• Sur la B-stabilité des méthodes de Runge-Kutta
• Reducibility and contractivity of Runge-Kutta methods revisited
• Stability Criteria for Implicit Runge–Kutta Methods
• Numerical Integration of Systems of Stiff Nonlinear Differential Equations
• Theorems on the Computation of the Transient Response of Nonlinear Networks Containing Transistors and Diodes

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