Efficient P-stable methods for periodic initial value problems

DOI10.1007/BF01937491zbMath0558.65053OpenAlexW2019221959MaRDI QIDQ762894

Jeff R. Cash

Publication date: 1984

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01937491

zbMATH Keywords

P-stabilityRunge-KuttaP-stable multistep formulae

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (18)

Efficient iterations for Gauss methods on second-order problems ⋮ Families of two-step fourth order \(P\)-stable methods for second order differential equations ⋮ Efficient fourth order P-stable formulae ⋮ A class of Rosenbrock-type schemes for second-order nonlinear systems of ordinary differential equations ⋮ Two-step hybrid methods for periodic initial value problems ⋮ Variable-order, variable-step methods for second-order initial-value problems ⋮ A modified numerov integration method for second order periodic initial-value problems ⋮ On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods ⋮ Solving second order initial value problems by a hybrid multistep method without predictors ⋮ A second-derivative functionally fitted method of maximal order for oscillatory initial value problems ⋮ High-order continuous third derivative formulas with block extensions fory″=f(x, y, y′) ⋮ The Hilber–Hughes–Taylor-α (HHT-α) method compared with an implicit Runge–Kutta for second-order systems ⋮ An Efficient Fourth Order Implicit Runge-Kutta Algorithm for Second Order Systems ⋮ An efficient implicit Runge-Kutta method for second order systems ⋮ On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods ⋮ Evaluating numerical ODE/DAE methods, algorithms and software ⋮ High accuracy hybrid formula for \(y= f(x,y)\) ⋮ Analysis of a class of multi-stage, multistep Runge-Kutta methods

Cites Work

• High order P-stable formulae for the numerical integration of periodic initial value problems
• Unconditionally stable methods for second order differential equations
• Stabilization of Cowell's method
• Symmetric Multistip Methods for Periodic Initial Value Problems
• On accuracy and unconditional stability of linear multistep methods for second order differential equations
• Two-step fourth order P-stable methods for second order differential equations
• Two-step fourth order P-stable methods for second order differential equations

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