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Numerical PDE
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Numerical methods for partial differential equations
Finite difference
Parabolic
Forward-time central-space
(FTCS)
Crank–Nicolson
Hyperbolic
Lax–Friedrichs
Lax–Wendroff
MacCormack
Upwind
Method of characteristics
Others
Alternating direction-implicit
(ADI)
Finite-difference time-domain
(FDTD)
Finite volume
Godunov
High-resolution
Monotonic upstream-centered
(MUSCL)
Advection upstream-splitting
(AUSM)
Riemann solver
Essentially non-oscillatory
(ENO)
Weighted essentially non-oscillatory
(WENO)
Finite element
hp-FEM
Extended
(XFEM)
Discontinuous Galerkin
(DG)
Spectral element
(SEM)
Mortar
Gradient discretisation
(GDM)
Loubignac iteration
Smoothed
(S-FEM)
Meshless/Meshfree
Smoothed-particle hydrodynamics
(SPH)
Peridynamics
(PD)
Moving particle semi-implicit method
(MPS)
Material point method
(MPM)
Particle-in-cell
(PIC)
Domain decomposition
Schur complement
Fictitious domain
Schwarz alternating
additive
abstract additive
Neumann–Dirichlet
Neumann–Neumann
Poincaré–Steklov operator
Balancing
(BDD)
Balancing by constraints
(BDDC)
Tearing and interconnect
(FETI)
FETI-DP
Others
Spectral
Pseudospectral
(DVR)
Method of lines
Multigrid
Collocation
Level-set
Boundary element
Method of moments
Immersed boundary
Analytic element
Isogeometric analysis
Infinite difference method
Infinite element method
Galerkin method
Petrov–Galerkin method
Validated numerics
Computer-assisted proof
Integrable algorithm
Method of fundamental solutions
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