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 ?
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
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.
The resolution of Laplace's Equation (1) in regions V, VI and VII by using the technique of separation of variables permits to get
In this section I introduced the hybrid separation of variables method (HSVM) to get the solution of equations (11) and (12).
In effect, we develop a quadrature formula to evaluate the integral equation using a separation of variables technique.
We do not assume separation of variables and we start with an empirical representation for the whole of the S-shaped cure-time curves.
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.
It lists additional mathematical models based on partial differential equations and shows how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace.
Brown (Emory University) explains the separation of variables technique and three numerical methods for solving linear first-order differential equations as well as graphical techniques for analyzing systems of differential equations.

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