On the solvability of the systems of equations arising in implicit Runge- Kutta methods

DOI10.1007/BF01954903zbMath0661.65078OpenAlexW2119589852MaRDI QIDQ1113625

S. H. Smith

Publication date: 1988

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01954903

zbMATH Keywords

stiff systemsimplicit Runge-Kutta methodsm-stage Lobatto III C methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations ⋮ 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 ⋮ 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 ⋮ Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments ⋮ An efficient implicit Runge-Kutta method for second order systems ⋮ An algebraic characterization of B-convergent Runge-Kutta methods

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