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.
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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
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
Spiral steps: the spirals unique characteristics may help disabled people get where they're going
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
The resolution of Laplace's Equation (1) in regions V, VI and VII by using the technique of separation of variables permits to get
Magnetic field distribution and levitation force calculation in HTSC-PMG maglev vehicles
In this section I introduced the hybrid separation of variables method (HSVM) to get the solution of equations (11) and (12).
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
We do not assume separation of variables and we start with an empirical representation for the whole of the S-shaped cure-time curves.
Thermal diffusivity
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
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.
Solution techniques for elementary partial differential equations, 2d ed
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.
Differential equations; a modeling approach

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