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New in Mathematica 10
Solving Partial Differential Equations with Finite Elements
Classical Partial Differential Equations
The Coefficient Form of Partial Differential Equations
What types of equations can be solved with the finite element method as implemented in NDSolve? Consider a single linear partial differential equation in :
The PDE is defined in . Here
is the dependent variable for which a solution is sought. The coefficients
,
,
, and
are scalars;
,
, and
are vectors; and
is an
×
matrix.
Systems of Partial Differential Equations
The Coefficient Form of Systems of Partial Differential Equations
Consider a system of two equations with dependent variables and
:
For a region in
, each
is an
×
matrix, and each of
,
, and
are vectors.
Sources: http://reference.wolfram.com/language/FEMDocumentation/tutorial/SolvingPDEwithFEM.html#509267359
http://reference.wolfram.com/language/FEMDocumentation/tutorial/FiniteElementOverview.html
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