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  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
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.