List of partial differential equation topics

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This is a list of partial differential equation topics, by Wikipedia page.

Contents 1 General topics 2 Specific partial differential equations 3 Numerical methods for PDEs 4 Related areas of mathematics

General topics

• Partial differential equation
• 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

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
• Maxwell's equations
• Navier-Stokes equations
• Poisson's equation
• Primitive equations (hydrodynamics)
• Schrödinger equation
• Wave equation

For a more complete list of named equations, see list of equations.

Numerical methods for PDEs

• Finite difference
• Finite element method
• Finite volume method
• Boundary element method
• Multigrid
• Spectral method
• Computational fluid dynamics

Related areas of mathematics

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

See in general list of numerical analysis topics.