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  2. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    Download as PDF; Printable version ... and partial differential equations. ... in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 ...

  3. 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.

  4. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

  5. Method of lines - Wikipedia

    en.wikipedia.org/wiki/Method_of_lines

    Thus it cannot be used directly on purely elliptic partial differential equations, such as Laplace's equation. However, MOL has been used to solve Laplace's equation by using the method of false transients. [1] [8] In this method, a time derivative of the dependent variable is added to Laplace’s equation. Finite differences are then used to ...

  6. Confluent hypergeometric function - Wikipedia

    en.wikipedia.org/wiki/Confluent_hypergeometric...

    Since Kummer's equation is second order there must be another, independent, solution. The indicial equation of the method of Frobenius tells us that the lowest power of a power series solution to the Kummer equation is either 0 or 1 − b. If we let w(z) be = then the differential equation gives

  7. Differential-algebraic system of equations - Wikipedia

    en.wikipedia.org/wiki/Differential-algebraic...

    In mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. The set of the solutions of such a system is a differential algebraic variety , and corresponds to an ideal in a differential algebra of differential ...

  8. Lie point symmetry - Wikipedia

    en.wikipedia.org/wiki/Lie_point_symmetry

    Lie point symmetry is a concept in advanced mathematics.Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations [1] [2] [3] (ODEs).

  9. Integro-differential equation - Wikipedia

    en.wikipedia.org/wiki/Integro-differential_equation

    Consider the following second-order problem, ′ + + = () =, where = {,, <is the Heaviside step function.The Laplace transform is defined by, = {()} = ().Upon taking term-by-term Laplace transforms, and utilising the rules for derivatives and integrals, the integro-differential equation is converted into the following algebraic equation,