Contributions to the development of differential systems exactly solved by multistep finite-difference schemes

DOI10.1016/j.amc.2010.05.101zbMath1201.65132OpenAlexW1973448807MaRDI QIDQ711298

Higinio Ramos

Publication date: 25 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.05.101

zbMATH Keywords

numerical examplesinitial value problemstrapezoidal ruleNumerov methodnonstandard finite-difference methodsexact finite-difference methodstwo-step Adams-Bashforth method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite difference and finite volume methods for ordinary differential equations (65L12)

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 ⋮ Unnamed Item ⋮ On Vergnaud's time integration method for autocatalytic cure rate equations ⋮ An efficient variable step-size rational Falkner-type method for solving the special second-order IVP ⋮ Solving first-order initial-value problems by using an explicit non-standard \(A\)-stable one-step method in variable step-size formulation ⋮ DEVELOPMENT OF A NONLINEAR HYBRID NUMERICAL METHOD

Uses Software

• Mathematica

Cites Work

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• Rational one-step methods for initial value problems
• Difference schemes of optimum degree of implicitness for a family of simple ODEs with blow-up solutions
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• Given a one-step numerical scheme, on which ordinary differential equations is it exact?
• A non-standard explicit integration scheme for initial-value problems
• ANALYSIS OF A FINITE-DIFFERENCE SCHEME FOR A LINEAR ADVECTION–DIFFUSION–REACTION EQUATION
• Solving Ordinary Differential Equations I
• Best difference equation approximation to Duffing's equation
• Nonlinear difference equations
• Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator
• Semidiscretization in Time of Nonlinear Parabolic Equations with Blowup of the Solution

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