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

NeumannBoundaryUnitNormal — specify a unit normal in Neumann conditions

PeriodicBoundaryCondition — specify periodic boundary conditions

Geometric Regions »

{x,y,…}∈Ω — specify the region for the independent variables

Disk  ▪  Ball  ▪  ImplicitRegion  ▪  MeshRegion  ▪  BoundaryMeshRegion  ▪  ...