Coefficients for Systems of PDEs

As Systems of PDEs describes, toolbox functions can address the case of systems of N PDEs. How do you represent the coefficients of your PDE in the correct form? In general, an elliptic system is


For 2-D systems, the notation (cu) represents an N-by-1 matrix with an (i,1)-component


For 3-D systems, the notation (cu) represents an N-by-1 matrix with an (i,1)-component


The symbols a and d denote N-by-N matrices, and f denotes a column vector of length N.

Other problems with N > 1 are the parabolic system


the hyperbolic system


and the eigenvalue system


To solve a PDE using this toolbox, you convert your problem into one of the forms the toolbox accepts. Then express your problem coefficients in a form the toolbox accepts.

The question is how to express each coefficient: d, c, a, and f. For answers, see f Coefficient for Systems, c Coefficient for Systems, and a or d Coefficient for Systems.

    Note:   If any coefficient depends on time or on the solution u or its gradient, then all coefficients should be NaN when either time or the solution u is NaN. This is the way that solvers check to see if the equation depends on time or on the solution.

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