A numerical ODE solver that preserves the fixed points and their stability

DOI10.1016/j.cam.2010.07.004zbMath1209.65072OpenAlexW2011209457MaRDI QIDQ629422

Higinio Ramos, Jesus Vigo Aguiar

Publication date: 9 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2010.07.004

zbMATH Keywords

stabilityfixed pointsnumerical examplespredictor-corrector methodinitial-value problemsexact finite difference methodsnonstandard finite-difference 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) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

Related Items (12)

Exact solutions of non-linear Klein-Gordon equation with non-constant coefficients through the trial equation method ⋮ Using the blow-up technique for a modified Lindemann mechanism ⋮ Diagonally implicit block backward differentiation formulas for solving ordinary differential equations ⋮ New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation ⋮ A new class of two-step P-stable TFPL methods for the numerical solution of second-order IVPs with oscillating solutions ⋮ A new four-step P-stable Obrechkoff method with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation ⋮ New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation ⋮ Exponentially fitted TDRK pairs for the Schrödinger equation ⋮ Two-frequency trigonometrically-fitted and symmetric linear multi-step methods for second-order oscillators ⋮ An explicit third-order one-step method for autonomous scalar initial value problems of first order based on quadratic Taylor approximation ⋮ Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes ⋮ A new implicit six-step P-stable method for the numerical solution of Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear multistep methods for initial value problems
• On the change of step size in multistep codes
• Control of local error stabilizes integrations
• 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
• Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator
• Exact finite-difference schemes for first order differential equations having three distinct fixed-points
• On the use of nonstandard finite difference methods†

This page was built for publication: A numerical ODE solver that preserves the fixed points and their stability