Category
page 1Numerical differential equations
finite element method
numerical method for solving physical or engineering problems
Runge–Kutta method
family of implicit and explicit iterative methods
Euler method
an explicit, first-order method for numerically solving ordinary differential equations
finite difference
discrete analog of a derivative
finite difference method
numerical methods for solving differential equations by approximating them with difference equations
Laplacian matrix
matrix representation of a graph
finite-volume method
method for representing and evaluating partial differential equations
numerical method for ordinary differential equations
methods used to find numerical solutions of ordinary differential equations
Smoothed-particle hydrodynamics
method of hydrodynamics simulation
linear multistep method
effective tools for solving ordinary equations, whose working principle is as follows: first we choose a starting point, and then take a small step forward to find the next solution point.
finite-difference time-domain method
numerical methods for solving partial differential equations
Galerkin method
class of methods for converting a continuous operator problem to a discrete problem
Crank–Nicolson method
finite difference method for numerically solving parabolic differential equations
Discrete element method
numerical method
Courant–Friedrichs–Lewy condition
mathematical condition for convergence
boundary element method
numerical computational method
Heun's method
The numerical procedure for solving ordinary differential equations with a given initial value created by Karl Heun.
shooting method
method for solving boundary value problems
Direct stiffness method
structural analysis technique; implementation of the finite element method
spectral method
class of methods used in numerical analysis, scientific computing to solve ODE/PDE
stiff equation
differential equation for which some numerical methods are unsustainable unless the step size is extremely small even though the solution is smooth, due to terms that can lead to rapid variation in the solution
finite difference coefficient
Coefficient used in numerical approximation
volume of fluid method
free-surface modelling technique
numerical method for partial differential equations
class of methods for solving partial differential equations
Lax equivalence theorem
theorem that asserts that a consistent and stable numerical method is convergent
list of Runge–Kutta methods
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Euler–Maruyama method
method for the approximate numerical solution of stochastic differential equations
backward Euler method
numerical method for solving differential equations
midpoint methods
a pair of one-step numeric methods for solving differential equations
Rayleigh–Ritz method
method for approximating eigenvalues
meshfree method
method in numerical analysis not requiring knowledge of neighboring points
discrete Laplace operator
analog of the continuous Laplace operator
Numerov's method
mathematical method to solve ordinary differential equations
mesh generation
dividing a geometric space into discrete cells
FTCS scheme
method for numerically solving parabolic partial differential equations
Newmark-beta method
Concept in differential equation mathematics
symplectic integrator
numerical integration scheme for Hamiltonian systems
Runge–Kutta–Fehlberg method
numerical algorithm for the solution of ordinary differential equations
method of lines
numerical method for solving partial differential equations
Dormand–Prince method
an embedded Runge-Kutta method for numerically solving differential equations
weak formulation
theorem
explicit and implicit methods
approaches for approximating solutions to differential equations
Particle-in-cell
In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points.
Semi-implicit Euler method
modification of the Euler method for solving Hamilton's equations