Partial differential equation with variable coefficients

Asked Dec 02 '20 at 13:35

Active Dec 10 '20 at 02:52

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I am stuck with the following problem.

I know how to solve the following partial differential equation $$\frac{\partial u(x,t)}{\partial t} +A(x,t) \frac{\partial^2 u(x,t)}{\partial^2 x}+ B(x,t) \frac{\partial u(x,t)}{\partial x} - Cu(x,t)=0,$$ if $A(x,t)=A$ and $B(x,t)=B$ are constants for all $(x,t)$ and I have some boundary conditions (note that $C$ is also a constant).

However, what if $A$ and $B$ are variable (i.e. they are functions of $x$ and $t$)? What is then the correct approach to solve this PDE with variable coefficients?

edited Dec 10 '20 at 02:52

Robert Howard

2,753

asked Dec 02 '20 at 13:35

mathlay

1

Explicitly or numerically? You need boundary/initial conditions. – xpaul Dec 03 '20 at 13:58
Explicitly. Is it not possible to find the general solution without having an explicit boundary solution? – mathlay Dec 04 '20 at 12:47

Partial differential equation with variable coefficients

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