The dimension n of the unknown x varies greatly, depending on the kind of problem. The dimension n is typically of the order:

10¹ -- 10² for intrinsically discrete, algebraic problems

10² -- 10³ for discretizations of ordinary differential equation boundary value problems

10³ -- 10^k for discretizations of partial differential equation boundary value problems

When such solutions are computed at a mesh of parameter values, the size of data files can quickly become an issue.
 

 

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