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  2. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function (s) and involves the derivatives of those functions. [ 1 ]

  3. Numerical methods for ordinary differential equations

    en.wikipedia.org/wiki/Numerical_methods_for...

    Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.

  4. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y ), which, therefore, depends on x .

  5. Euler method - Wikipedia

    en.wikipedia.org/wiki/Euler_method

    It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler , who first proposed it in his book Institutionum calculi integralis (published 1768–1770).

  6. List of nonlinear ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/List_of_nonlinear_ordinary...

    Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations.

  7. Method of characteristics - Wikipedia

    en.wikipedia.org/wiki/Method_of_characteristics

    The method is to reduce a partial differential equation (PDE) to a family of ordinary differential equations (ODE) along which the solution can be integrated from some initial data given on a suitable hypersurface.

  8. Method of undetermined coefficients - Wikipedia

    en.wikipedia.org/wiki/Method_of_undetermined...

    Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]

  9. Lorenz system - Wikipedia

    en.wikipedia.org/wiki/Lorenz_system

    A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = ⁠ 8 / 3 ⁠. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz.

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