A two-step explicit \(P\)-stable method for solving second order initial value problems.

DOI10.1016/S0096-3003(02)00154-6zbMath1042.65056MaRDI QIDQ1406151

Qinghong Li, Xin-Yuan Wu

Publication date: 9 September 2003

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

zbMATH Keywords

initial value problemcharacteristic equationP-stabilityexplicit two-step method

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 (10)

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 ⋮ A two-step explicit \(P\)-stable method of high phase-lag order for second order IVPs. ⋮ Oscillations of solutions of second-order quasilinear differential equations with impulses ⋮ 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 ⋮ On the stability of a two-step method for solving periodic IVPs ⋮ Two-step explicit methods for second-order IVPs with oscillatory solutions

Cites Work

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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 \(y=f(t,y)\)
• Unconditionally stable methods for second order differential equations
• On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods
• 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)
• Symmetric Multistip Methods for Periodic Initial Value Problems

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