Integral Equation

In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Maxwell's equations.

Read more about Integral EquationOverview, Numerical Solution, Classification, Integral Equations As A Generalization of Eigenvalue Equations

Other articles related to "integral equation, equation, integral equations, equations, integral":

Boundary Element Method - Mathematical Basis
... The integral equation may be regarded as an exact solution of the governing partial differential equation ... method attempts to use the given boundary conditions to fit boundary values into the integral equation, rather than values throughout the space defined ... Once this is done, in the post-processing stage, the integral equation can then be used again to calculate numerically the solution directly at any desired point in the interior of the solution domain ...
Integral Equations As A Generalization of Eigenvalue Equations
... Certain homogeneous linear integral equations can be viewed as the continuum limit of eigenvalue equations ... Using index notation, an eigenvalue equation can be written as , where is a matrix, is one of its eigenvectors, and is the associated eigenvalue ... and with continuous variables and, gives , where the sum over has been replaced by an integral over and the matrix and vector have been replaced by the 'kernel ...
Stochastic Differential Equation - Use in Probability and Mathematical Finance
... on numerical methods for solving stochastic differential equations ... A typical equation is of the form where denotes a Wiener process (Standard Brownian motion) ... This equation should be interpreted as an informal way of expressing the corresponding integral equation The equation above characterizes the behavior of the continuous time ...
Weierstrass's Elliptic Functions - Integral Equation
... The Weierstrass elliptic function can be given as the inverse of an elliptic integral ... Then one has The above follows directly by integrating the differential equation ...

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