Template: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)

Godunov
High-resolution
Monotonic upstream-centered (MUSCL)
Advection upstream-splitting (AUSM)
Riemann solver
Essentially non-oscillatory (ENO)
Weighted essentially non-oscillatory (WENO)

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

Template:Documentation

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