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.
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References in periodicals archive ?
Separation of variables method is applied to solve the problem in the model.
Multiphase-interacting equations and their solutions in simulation of coalbed gas migration
Kostoglou, "On the analytical separation of variables solution for a class of partial integro-differential equations," Applied Mathematics Letters, vol.
Sherman-Morrison-Woodbury Formula for Linear Integrodifferential Equations
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[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.
Exact analytical solution for 3D time-dependent heat conduction in a multilayer sphere with heat sources using eigenfunction expansion method
In this paper, we reinforced the method of separation of variables from [1] and developed the forced vibration method from [3].
Discussion of the improved methods for analyzing a cantilever beam carrying a tip-mass under base excitation
The resolution of Laplace's Equation (1) in regions V, VI and VII by using the technique of separation of variables permits to get
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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.
Dual phase lag heat conduction and thermoelastic properties of a semi-infinite medium induced by ultrashort pulsed laser
In effect, we develop a quadrature formula to evaluate the integral equation using a separation of variables technique.
Iterative sinc-convolution method for solving radiosity equation in computer graphics
The usual approach is to assume separation of variables and to work in terms of an equivalent cure time at an arbitrary reference temperature.
Thermal diffusivity
In order to achieve the separation of variables, we set
Expanded (G/[G.sup.2]) Expansion Method to Solve Separated Variables for the 2+1-Dimensional NNV Equation
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."
Fourier series and numerical methods for partial differential equations

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