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

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 (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