Category:Numerical differential equations

• Numerical methods for ordinary differential equations
• Numerical methods for partial differential equations

*

• Numerical methods for differential equations

A

• Adaptive mesh refinement
• Adaptive step size
• Advection upstream splitting method
• Alternating-direction implicit method
• Analytic element method

B

• Backward differentiation formula
• Backward Euler method
• Beam and Warming scheme
• Beeman's algorithm
• Bi-directional delay line
• Boundary element method
• Boundary knot method
• Boundary particle method

C

• Cash–Karp method
• Céa's lemma
• Cell lists
• Central differencing scheme
• Characteristic mode analysis
• Collocation method
• Compact stencil
• Composite methods for structural dynamics
• Constraint (computational chemistry)
• Coupled mode theory
• Courant–Friedrichs–Lewy condition
• Crank–Nicolson method
• Cyclic reduction

D

• Diffuse element method
• Direct multiple shooting method
• Direct stiffness method
• Discontinuous Galerkin method
• Discrete calculus
• Discrete element method
• Discrete Laplace operator
• Discrete Poisson equation
• Dormand–Prince method

E

• Eigenvalues and eigenvectors of the second derivative
• Energy drift
• ENO methods
• Euler method
• Euler–Maruyama method
• Explicit and implicit methods
• Exponential integrator
• Extended discrete element method
• Extended finite element method

F

• False diffusion
• Fast marching method
• Fast multipole method
• Fast sweeping method
• Finite difference
• Finite difference coefficient
• Finite difference method
• Finite difference methods for option pricing
• Finite element method
• Dynamic design analysis method
• Finite element method in structural mechanics
• Finite pointset method
• Finite volume method
• Finite-difference frequency-domain method
• Finite-difference time-domain method
• Five-point stencil
• Flux limiter
• FTCS scheme

G

• Galerkin method
• General linear methods
• Geometric integrator
• Godunov's scheme
• Godunov's theorem
• Gradient discretisation method

H

• Heun's method
• High-resolution scheme
• Higher-order compact finite difference scheme
• History of numerical solution of differential equations using computers

I

• Immersed boundary method
• Infinite difference method
• Infinite element method
• Interval boundary element method

K

• Kronecker sum of discrete Laplacians

L

• L-stability
• Laplacian matrix
• Lax equivalence theorem
• Lax–Friedrichs method
• Lax–Wendroff method
• Lax–Wendroff theorem
• Leapfrog integration
• Leimkuhler–Matthews method
• Linear multistep method
• Loubignac iteration

M

• MacCormack method
• Material point method
• Mesh generation
• Meshfree methods
• Method of fundamental solutions
• Method of lines
• Method of moments (electromagnetics)
• Microscale and macroscale models
• Midpoint method
• Milstein method
• Mimesis (mathematics)
• Modal analysis using FEM
• Momentum (electromagnetic simulator)
• Moving particle semi-implicit method
• Multilevel fast multipole method
• Multiphase particle-in-cell method
• Multisymplectic integrator
• MUSCL scheme

N

• Natural element method
• Newmark-beta method
• Nine-point stencil
• Non-compact stencil
• Numerical diffusion
• Numerical dispersion
• Numerical resistivity
• Numerov's method

P

• P-FEM
• Pantelides algorithm
• Parareal
• Partial element equivalent circuit
• Particle method
• Particle-in-cell
• Perfectly matched layer
• Principles of grid generation
• Proper orthogonal decomposition

Q

• Quantized state systems method

R

• Raviart–Thomas basis functions
• Rayleigh–Ritz method
• Regularized meshless method
• Roe solver
• Runge–Kutta method (SDE)
• List of Runge–Kutta methods
• Runge–Kutta methods
• Runge–Kutta–Fehlberg method

S

• Semi-implicit Euler method
• Shock-capturing method
• Shooting method
• Singular boundary method
• Smoothed finite element method
• Smoothed-particle hydrodynamics
• Spectral element method
• Spectral method
• Split-step method
• Stencil (numerical analysis)
• Stiff equation
• Stochastic Eulerian Lagrangian method
• Strang splitting
• Stretched grid method
• Symplectic integrator

T

• Total variation diminishing
• Trefftz method

U

• Uniform theory of diffraction
• Upwind differencing scheme for convection
• Upwind scheme

V

• Variational integrator
• Verlet integration
• Virtual Cell
• Volume of fluid method
• Vorticity confinement

W

• Walk-on-spheres method
• Weak formulation
• Weakened weak form
• WENO methods

Z

• Zero stability