When.com Web Search

Search results

  1. Results From The WOW.Com Content Network
  2. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    Sturm–Liouville theory is a theory of a special type of second-order linear ordinary differential equation. Their solutions are based on eigenvalues and corresponding eigenfunctions of linear operators defined via second-order homogeneous linear equations .

  3. Sturm–Liouville theory - Wikipedia

    en.wikipedia.org/wiki/Sturm–Liouville_theory

    The differential equation is said to be in Sturm–Liouville form or self-adjoint form.All second-order linear homogenous ordinary differential equations can be recast in the form on the left-hand side of by multiplying both sides of the equation by an appropriate integrating factor (although the same is not true of second-order partial differential equations, or if y is a vector).

  4. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.

  5. List of nonlinear ordinary differential equations - Wikipedia

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

    Order Equation Application Reference Abel's differential equation of the first kind: 1 = + + + Class of differential equation which may be solved implicitly [1] Abel's differential equation of the second kind: 1

  6. Numerical methods for ordinary differential equations - Wikipedia

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

    For example, the second-order equation y′′ = −y can be rewritten as two first-order equations: y′ = z and z′ = −y. In this section, we describe numerical methods for IVPs, and remark that boundary value problems (BVPs) require a different set of tools. In a BVP, one defines values, or components of the solution y at more than one ...

  7. Euler–Lagrange equation - Wikipedia

    en.wikipedia.org/wiki/Euler–Lagrange_equation

    In the calculus of variations and classical mechanics, the Euler–Lagrange equations [1] are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange.

  8. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    Runge–Kutta–Nyström methods are specialized Runge–Kutta methods that are optimized for second-order differential equations. [22] [23] A general Runge–Kutta–Nyström method for a second-order ODE system ¨ = (,, …,) with order is with the form

  9. Second-order - Wikipedia

    en.wikipedia.org/wiki/Second-order

    Second order approximation, an approximation that includes quadratic terms; Second-order arithmetic, an axiomatization allowing quantification of sets of numbers; Second-order differential equation, a differential equation in which the highest derivative is the second; Second-order logic, an extension of predicate logic