List of partial differential equation topics
# List of partial differential equation topics

This is a list of partial differential equation topics.

## General topics

* Partial differential equation
   * Nonlinear partial differential equation
      * list of nonlinear partial differential equations
* Boundary condition
* Boundary value problem
   * Dirichlet problem, Dirichlet boundary condition
   * Neumann boundary condition
   * Stefan problem
   * Wiener–Hopf problem
* Separation of variables
* Green's function
* Elliptic partial differential equation
* Singular perturbation
* Cauchy–Kovalevskaya theorem
* H-principle
* Atiyah–Singer index theorem
* Bäcklund transform
* Viscosity solution
* Weak solution
* Loewy decomposition of linear differential equations

## Specific partial differential equations

* Broer–Kaup equations
* Burgers' equation
* Euler equations
* Fokker–Planck equation
* Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation
* Heat equation
* Laplace's equation
   * Laplace operator
   * Harmonic function
   * Spherical harmonic
   * Poisson integral formula
* Klein–Gordon equation
* Korteweg–de Vries equation
   * Modified KdV–Burgers equation
* Maxwell's equations
* Navier–Stokes equations
* Poisson's equation
* Primitive equations (hydrodynamics)
* Schrödinger equation
* Wave equation

## Numerical methods for PDEs

* Finite difference
* Finite element method
* Finite volume method
* Boundary element method
* Multigrid
* Spectral method
* Computational fluid dynamics
* Alternating direction implicit

## Related areas of mathematics

* Calculus of variations
* Harmonic analysis
* Ordinary differential equation
* Sobolev space
