Backward Euler method - Wikipedia
https://en.wikipedia.org/wiki/Backward_Euler_methodDescription. Consider the ordinary differential equation = (,) with initial value () =. Here the function and the initial data and are known; the function depends on the real variable and is unknown. A numerical method produces a sequence ,,, … such that approximates (+), where is called the step size.. The backward Euler method computes the approximations using
Backward Euler Method - Prof. Michael T. Heath
heath.cs.illinois.edu › iem › odeSpecifically, from an approximate solution value yk at time tk for an ODE y ′ = f ( t, y), the Backward Euler method approximates the solution y ( tk+1) at time tk+1 = tk + hk by solving the implicit equation yk+1 = yk + hk f ( tk+1 , yk+1) for yk+1. Since this equation may be nonlinear, solving it in general requires an iterative solution ...
Euler Backward Method -- from Wolfram MathWorld
mathworld.wolfram.com › EulerBackwardMethodDec 17, 2021 · Euler Backward Method. An implicit method for solving an ordinary differential equation that uses in . In the case of a heat equation, for example, this means that a linear system must be solved at each time step. However, unlike the Euler forward method, the backward method is unconditionally stable and so allows large time steps to be taken.