On the stability of rational Runge Kutta methods

DOI10.1016/0771-050X(82)90054-7zbMath0495.65032OpenAlexW2045909350MaRDI QIDQ1169795

M. Mar Quemada, Manuel Calvo

Publication date: 1982

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0771-050x(82)90054-7

zbMATH Keywords

stiff differential systemsrational Runge Kutta methods

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)

Related Items (7)

\(L\)-stable explicit nonlinear method with constant and variable step-size formulation for solving initial value problems ⋮ An embedded 3(2) pair of nonlinear methods for solving first order initial-value ordinary differential systems ⋮ Numerical experiments on the rational Runge-Kutta method ⋮ Solving first-order initial-value problems by using an explicit non-standard \(A\)-stable one-step method in variable step-size formulation ⋮ A note on contractivity in the numerical solution of initial value problems ⋮ Convergence of the Lambert-McLeod trajectory solver and of the CELF method ⋮ Rational Runge-Kutta methods are not suitable for stiff systems of ODEs

Cites Work

• Solution of the equations associated with rational Runge-Kutta methods of orders up to four
• Unconditionally stable explicit methods for parabolic equations
• Nonlinear methods in solving ordinary differential equations
• Rational Runge-Kutta methods for solving systems of ordinary differential equations
• [https://portal.mardi4nfdi.de/wiki/Publication:5339699 On the Numerical Solution of y � = f(x, y) by a Class of Formulae Based on Rational Approximation]

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