The Wolfram Language has powerful functionality based on the finite element method and the numerical method of lines for solving a wide variety of partial differential equations. The symbolic capabilities of the Wolfram Language make it possible to efficiently compute solutions from PDE models expressed as equations.
Inactive — represent an operator in an inactive form
NDSolve — numerical solution to partial differential equations over a region
NDEigensystem — numerical eigenvalues and eigenfunctions to PDE over a region
DSolve — symbolic solution to partial differential equations over a region
DEigensystem — symbolic eigenvalues and eigenfunctions to PDE over a region
DirichletCondition — specify Dirichlet conditions for partial differential equations
NeumannValue — specify Neumann and Robin conditions