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I have a PDE of the following form:

[tex] f_t(t,x,y) = k f + g(x,y) f_x(t,x,y) + h(x,y) f_y(t,x,y) + c f_{yy}(t,x,y) \\

\lim_{t\to s^+} f(t,x,y) = \delta (x-y)[/tex]

Here [itex]k[/itex] and [itex]c [/itex] are real numbers and [itex]g, h[/itex] are (infinitely) smooth real-valued functions. I have been trying to learn how to do this numerically (was going to use MATLAB's pdepe function which uses a finite difference method, I believe), but I have no clue what to do regarding the boundary condition.

How does one numerically integrate a PDE with dirac delta boundary condition?

[tex] f_t(t,x,y) = k f + g(x,y) f_x(t,x,y) + h(x,y) f_y(t,x,y) + c f_{yy}(t,x,y) \\

\lim_{t\to s^+} f(t,x,y) = \delta (x-y)[/tex]

Here [itex]k[/itex] and [itex]c [/itex] are real numbers and [itex]g, h[/itex] are (infinitely) smooth real-valued functions. I have been trying to learn how to do this numerically (was going to use MATLAB's pdepe function which uses a finite difference method, I believe), but I have no clue what to do regarding the boundary condition.

How does one numerically integrate a PDE with dirac delta boundary condition?

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