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
• Euler equations
• 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
• 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