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Partial Differential Equations—Wolfram Language Documentation

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• Functions
  • Ball
  • BoundaryMeshRegion
  • Curl
  • D
  • DEigensystem
  • DEigenvalues
  • DirichletCondition
  • Disk
  • Div
  • DSolve
  • DSolveValue
  • Grad
  • ImplicitRegion
  • Inactive
  • Laplacian
  • MeshRegion
  • NDEigensystem
  • NDEigenvalues
  • NDSolve
  • NDSolveValue
  • NeumannValue
  • ParametricNDSolveValue
  • PeriodicBoundaryCondition
• Related Guides
  • Differential Equations
  • PDEModeling
  • Geometric Regions
  • Finite Element Method
  • Calculus
• Tech Notes
  • Partial Differential Equation Models
  • Numeric Solutions of PDEs
  • Symbolic Solutions of PDEs

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  ▪  ...

DirichletCondition — specify Dirichlet conditions for partial differential equations

NeumannValue — specify Neumann and Robin conditions

PeriodicBoundaryCondition — specify periodic boundary conditions

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

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

▪
• Partial Differential Equation Models
▪
• Numeric Solutions of PDEs
▪
• Symbolic Solutions of PDEs

▪
• Differential Equations
▪
• PDEModeling
▪
• Geometric Regions
▪
• Finite Element Method
▪
• Calculus

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