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  • Ordinary differential equations
    You are here: Modules > ODE's
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    ODE's

    Many dynamical systems in physics, astronomy, chemistry, physiology, meteorology, economics, population dynamics can be described by Ordinary Differential Equations.
    In the second half of the 20th century much attention has been focussed on the often chaotic, i.e. unpredictable behaviour of (non-linear) ODE's. A well-known example is the Lorenz atrractor, illustrating the "Butterfly effect": small causes can have large effects. Mathgrapher uses an accurate Adams-Bashforth variable order, variable step predictor-corrector algorithm to integrate systems of up to 20 coupled differential equations.

    Several analytical tools are available for ODE's such as:
    Time series Power spectra 2D and 3D projections Phase portraits Poincare section Equilibrium points Lyapunov exponents

    Examples:
    Lorenz Equations Hénon-Heiles potential Rössler Equation
    van der Pol oscillator    Duffing oscillator Predator-Prey equation (Voltera)

    ODEs: Analysis

    ODE's - Analysis

    Set the initial values, the T  Range, number of output steps, and perhaps the Error tolerance -- start the Integration by pushing the Integrate button. When the integration is done choose from the combo box the type of Graph you want to draw and push the Draw button.
     
     
     
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