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Mathematics
Differential Equations
Separation of variables for nonhomogeneous differential equation
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[QUOTE="jasonRF, post: 5827793, member: 192203"] Separation of variables is a technique useful for homogeneous problems. For your non-homogeneous problem you need another approach. However, even for the homogeneous version of your equation, it will be separable only for specific forms of ##\kappa(\mathbf{r})## and ##\mu(\mathbf{r})##, and for certain forms of the boundary conditions. Edit: note that the shapes of your boundaries must also be on surfaces of constant coordinates, otherwise separation of variables will not work. If your homogeneous problem is separable then you [I]might[/I] be able to take the standard approach of using eigenfunctions of the homogenous problem to solve the non-homogeneous problem. In particular, I would look at the eigenfunctions of the spatial part of your operator, and expand ##q## and ##\Phi## as a series with time-varying coefficients. For this to work at all, the equation with boundary conditions needs to be separable, the eigenfunctions need to be complete, and for practical reasons you hope the eigenfunctions are orthogonal. Otherwise you need another approach. good luck, jason [/QUOTE]
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Differential Equations
Separation of variables for nonhomogeneous differential equation
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