Efficient sixth order methods for nonlinear oscillation problems

DOI10.1007/BF01954909zbMath0667.65064OpenAlexW2031223160MaRDI QIDQ1117675

S. H. Smith

Publication date: 1988

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01954909

zbMATH Keywords

Newton iterationmatrix factorizationP- stabilitysixth order P-stable methodstwo-step (hybrid) methodsvariable step, local error controlling code

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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)

Variable-order, variable-step methods for second-order 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′) ⋮ On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods ⋮ High accuracy hybrid formula for \(y= f(x,y)\)

Cites Work

• Efficient fourth order P-stable formulae
• High order P-stable formulae for the numerical integration of periodic initial value problems
• Efficiency of Methods for Second-Order Problems
• High-accuracy P-stable Methods for y^″ = f(t, y)
• Implementation of Implicit Formulas for the Solution of ODE<scp>s</scp>
• Symmetric Multistip Methods for Periodic Initial Value Problems

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