Partial Differential Equations
TopicOverview »
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.
D ▪ Grad ▪ Div ▪ Curl ▪ Laplacian ▪ ...
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
NDSolveValue ▪ ParametricNDSolveValue ▪ NDEigenvalues ▪ ...
DSolve — symbolic solution to partial differential equations over a region
DEigensystem — symbolic eigenvalues and eigenfunctions to PDE over a region
DSolveValue ▪ DEigenvalues ▪ ...
Boundary Conditions
DirichletCondition — specify Dirichlet conditions for partial differential equations
NeumannValue — specify Neumann and Robin conditions
PeriodicBoundaryCondition — specify periodic boundary conditions
Geometric Regions »
{x,y,…}∈Ω — specify the region 
for the independent variables
Disk ▪ Ball ▪ ImplicitRegion ▪ MeshRegion ▪ BoundaryMeshRegion ▪ ...