11 articles
Backward differentiation formula
The backward differentiation formula (BDF) is a family of implicit linear multistep methods for stiff ordinary differential equations, first used in Curtiss and Hirschfelder's 1952 paper.
Backward Euler method
The backward Euler method, also called implicit Euler, is a first-order implicit method for integrating ordinary differential equations, valued for its stability on stiff problems.
Explicit time integration
Explicit time integration is a class of numerical methods that advance time-dependent differential equations step by step using only known values, favored for crash and shock simulation.
Exponential integrator
An exponential integrator is a time-stepping method for stiff or oscillatory semilinear differential equations that solves the linear part exactly through a matrix exponential, dating to the 1960s.
Exponential time differencing
Exponential time differencing (ETD) is a family of numerical methods for stiff semilinear differential equations that integrates the linear part exactly with matrix exponentials, dating to the 1960s.
Operator splitting
Operator splitting is a numerical time-integration method for ODEs and PDEs that applies sub-operators one after another, exact when they commute and otherwise carrying a splitting error.
Predictor–corrector method
A predictor–corrector method is a numerical method for solving ordinary differential equations: an explicit formula predicts the next step, and a more accurate implicit formula corrects it.
Runge–Kutta–Fehlberg method
The Runge–Kutta–Fehlberg method is an adaptive-step numerical method for ordinary differential equations, introduced by E. Fehlberg in 1968; its best-known instance, combining fourth- and fifth-order formulas, is RKF45.
Semi-implicit method
A semi-implicit method is a time-integration scheme for differential equations that treats stiff terms implicitly and the rest explicitly, gaining stability while avoiding iterative solvers.
Temporal discretization
Temporal discretization is the numerical technique of replacing time derivatives in differential equations with difference quotients at discrete time steps, so time-dependent equations can be solved by iterating an update formula.
Time stepping
Time stepping, also called the time-stepping method, is a numerical technique that advances solutions of time-dependent differential equations step by step, the standard way to solve initial value problems for ODEs.