A two-step explicit \(P\)-stable method of high phase-lag order for second order IVPs.

DOI10.1016/S0096-3003(03)00319-9zbMath1053.65052OpenAlexW2076028194MaRDI QIDQ1428397

Qinghong Li, Xin-Yuan Wu

Publication date: 29 March 2004

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(03)00319-9

zbMATH Keywords

numerical examplestwo-body problemerror boundP-stabilityharmonic oscillatorperiodic initial value problemssecond order equationsvector differential equationsexplicit two-step methods

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (9)

One-step explicit methods for the numerical integration of perturbed oscillators ⋮ Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs ⋮ A two-step explicit \(P\)-stable method of high phase-lag order for linear periodic IVPs ⋮ A new family of explicit linear two-step singularly P-stable Obrechkoff methods for the numerical solution of second-order IVPs ⋮ Piecewise-linearized methods for initial-value problems with oscillating solutions ⋮ A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems ⋮ A class of two-step explicit methods for periodic IVPs ⋮ Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs ⋮ Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods

Cites Work

• Unnamed Item
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• A four-step method for the numerical solution of the Schrödinger equation
• Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y=f(t,y)\)
• On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods
• A two-step explicit \(P\)-stable method for solving second order initial value problems.
• The vector form of a sixth-order \(A\)-stable explicit one-step method for stiff problems
• An explicit two-step method exact for the scalar test equation \(y'= \lambda y\)
• A sixth-order \(A\)-stable explicit one-step method for stiff systems
• High-accuracy P-stable Methods for y^″ = f(t, y)
• P-Stable Obrechkoff Methods with Minimal Phase-Lag for Periodic Initial Value Problems
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• Symmetric Multistip Methods for Periodic Initial Value Problems

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