# separation of variables

(redirected from Method of separation of variables)

## 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 ?
The solution of the homogeneous equation (8) can be easily found by a method of separation of variables, whereby the above equation can be written as:
Then, the eigenfunction expansion method is used to solve the nonhomogeneous steady-state subproblem and the method of separation of variables is used to solve the homogeneous transient subproblem.
1) by using the method of separation of variables and Fourier series analysis.
However, only Laplace Equation (1) is solved in all sub-domains by using the method of separation of variables.
The study is done as above with solving Equations (1) and (2) by using the method of separation of variables.
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.

Site: Follow: Share:
Open / Close