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Solve()

The syntax for a single unknown function u solution of a PDE is
solve(u) 
 begin 
   onbdy()...; 
   onbdy()...; 
   ...; 
   pde(u)... 
 end;

For 2-systems and the use of solve(u,v), see the section 2-Systems . It defines a PDE and its boundary conditions. It will be solved by the Finite Element Method of degree 1 on triangles and a Gauss factorization.

Once the matrix is built and factorized solve may be called again by solve(u,-1)...; then the matrix is not rebuilt nor factorized and only a solution of the linear system is performed by an up and a down sweep in the Gauss algorithm only. This saves a lot of CPU time whenever possible. Several matrices can be stored and used simultaneously, in which case the sequence is

solve(u,i)...;
... 
solve(u,-i)...;
where i is a scalar variable (not an array function).

However matrices must be constructed in the natural order: i=1 first then i=2.... after they can be re-used in any order. One can also re-use an old matrix with a new definition, as in

solve(u,i)...;
... 
solve(u,i)...;
solve(u,\pm i)...;
Notice that solve(u) is equivalent to solve(u,1) .

Remark: 2-Systems have their own matrices, so they do not count in the previous ordering.


next up previous contents index
Next: 2-Systems Up: Solving an equation Previous: Pde()   Contents   Index
Build Daemon 2001-10-22