In this study, the finite approximates equations in addition to non-explicit Euler method
were used for numerical solving of these equations.
In Section 2, the explicit Euler method
for an ordinary differential equation (ODE) initial value problem (IVP) is investigated under a parameter transformation.
In this paper we apply Runge-Kutta Heun method of order 3 to solve fuzzy differential equations and establish that this method is better than Euler method
The backward Euler method
and the trapezoidal method.
This paper establishes the kinematics model of quadrotor helicopter by Newton Euler method
, and obtains rotor lift model through experiment.
For example, the implicit Euler method
corresponds to [[beta].
The standard Euler method
has been used where the numerical method for solving FDEs is employed in [1, 2, 8].
Here, we use the unsteady linear advection equation as a model equation and discretize this with a finite volume scheme and the implicit Euler method
He reviews direct solutions of linear systems, then moves on to describing initial value ordinary differential equations, including the Euler method
, the initial value diffusion problem, the initial value transport and wave problems, boundary value problems, and the finite element methods.
2 Numerical blow-up times, numbers of iterations, CPU times (seconds), and orders of the approximations obtained with the first implicit Euler method
We observe that when M [right arrow] [infinity], then a, [beta] [right arrow] 1 and the stability region tends to that of the classical Euler method
, that is, the region outside the circle centered in (1, 0) and with radius equal to 1.
We also compare the ASR method with the Linearly Implicit Euler method
, based on solving an appropriate linear system involving the Jacobian of the nonlinear operator by using GMRES with the Additive Schwarz preconditioner as in ASR and we show that the ASR method is asymptotically less expensive.