title: List of partial differential equation topics
text: # 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
  