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