2-D Systems in the PDE App

You can enter coefficients for a system with N = 2 equations in the PDE app, see Systems of PDEs. To do so, open the PDE app and select Generic System.

Then select PDE > PDE Specification.

Enter string expressions for coefficients using the form in Coefficients for Scalar PDEs in PDE App, with additional options for nonlinear equations. The additional options are:

  • Represent the ith component of the solution u using 'u(i)' for i = 1 or 2.

  • Similarly, represent the ith components of the gradients of the solution u using 'ux(i)' and 'uy(i)' for i = 1 or 2.

    Note:   For elliptic problems, when you include coefficients u(i), ux(i), or uy(i), you must use the nonlinear solver. Select Solve > Parameters > Use nonlinear solver.

Do not use quotes or unnecessary spaces in your entries.

For higher-dimensional systems, do not use the PDE app. Represent your problem coefficients at the command line.

You can enter scalars into the c matrix, corresponding to these equations:

·(c11u1)·(c12u2)+a11u1+a12u2=f1·(c21u1)·(c22u2)+a21u1+a22u2=f2.

If you need matrix versions of any of the cij coefficients, enter expressions separated by spaces. You can give 1-, 2-, 3-, or 4-element matrix expressions. These mean:

  • 1-element expression: (c00c)

  • 2-element expression: (c(1)00c(2))

  • 3-element expression: (c(1)c(2)c(2)c(3))

  • 4-element expression: (c(1)c(3)c(2)c(4))

For details, see c for Systems.

For example, these expressions show one of each type (1-, 2-, 3-, and 4-element expressions)

These expressions correspond to the equations

·((4+cos(xy)004+cos(xy))u1)·((1001)u2)=1·((.1.2.2.3)u1)·((7.6.5exp(xy))u2)=2.

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