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,ħi)...;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.