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The two primary things that FlexPDE needs to know are:

•what are the variables that you want to analyze?

•what are the partial differential equations that define them?

The VARIABLES and EQUATIONS sections of a problem script supply this information. The two are closely linked, since you must have one equation for each variable in a properly posed system.

In a simple problem, you may have only a single variable, like voltage or temperature. In this case, you can simply state the variable and equation:

VARIABLES

Phi

EQUATIONS

Div(grad(Phi)) = 0

In a more complex case, there may be many variables and many equations. FlexPDE will want to know how to associate equations with variables, because some of the details of constructing the model will depend on this association.

Each equation must be labeled with the variable to which it is associated (name and colon), as indicated below:

VARIABLES

A,B

EQUATIONS

A: Div(grad(A)) = 0

B: Div(grad(B)) = 0

Later, when we specify boundary conditions, these labels will be used to associate boundary conditions with the appropriate equation.