# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Separation of variables method is applied to solve the problem in the model.
Kostoglou, "On the analytical separation of variables solution for a class of partial integro-differential equations," Applied Mathematics Letters, vol.
thesis what he did when he discovered the separation of variables idea: "I ecstatically jumped, pumped my fist, [and] jump shot my soft drink can into the trash can, while repeating the words, 'That's it!'" He could finally custom-design a wheel for any application.
Result showed there is significant relation between the mental health of women with diabetes Separation of variables: education, employment, marital status, economic status and disease duration and mental health.
[6] and Lu and Viljanen [7] combined separation of variables and Laplace transforms to solve the transient conduction in the two-dimensional cylindrical and spherical media.
In this paper, we reinforced the method of separation of variables from [1] and developed the forced vibration method from [3].
The resolution of Laplace's Equation (1) in regions V, VI and VII by using the technique of separation of variables permits to get
The problem is formulated in the dimensionless form and then solved analytically by inventing a new sort of the separation of variables hybridized by the source structure function.
In effect, we develop a quadrature formula to evaluate the integral equation using a separation of variables technique.
The usual approach is to assume separation of variables and to work in terms of an equivalent cure time at an arbitrary reference temperature.
Bernatz (mathematics, Luther College, Iowa) introduces solution techniques of separation of variables, orthogonal eigenfunction bases, and Fourier solutions, as well as the following advanced numerical solution techniques for nonlinear problems: the finite difference method, the finite element method, and "the finite analytic method wherein separation of variables Fourier series methods are applied to locally linearized versions of the original partial differential equations."

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