separation of variables

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separation of variables

[‚sep·ə′rā·shən əv ′ver·ē·ə·bəlz]
(mathematics)
A technique where certain differential equations are rewritten in the form ƒ(x) dx = g (y) dy which is then solvable by integrating both sides of the equation.
A method of solving partial differential equations in which the solution is written in the form of a product of functions, each of which depends on only one of the independent variables; the equation is then arranged so that each of the terms involves only one of the variables and its corresponding function, and each of these terms is then set equal to a constant, resulting in ordinary differential equations. Also known as product-solution method.
References in periodicals archive ?
In the next section, we illustrate the sinc-convolution algorithm using the method of separation of variables.
Here, we enlist the method of separation of variables for solving the two-dimensional convolution-type integrals defined in (3.

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