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The motion is updated in time by using the backward difference formula through an iterative procedure.
The equations of motion and of design sensitivity are discritized by using the backward difference formula (BDF) in time domain.
First order derivatives: (a) using the forward difference, (b) using the backward difference, (c) using the central difference.
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The estimator assumes that the nonlinear function is slowly varying and that the observer converges quickly and uses the backward difference formula to approximate the state derivative.
Therefore, we used the backward differencing solver ode15s to accommodate the inherent stiffness of the MRL model.
Now, using the backward substitution, we obtain (4.8).
The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula.
The backward difference formula (BDF) class of multi-step schemes has been widely used as time integration method for both ordinary and partial differential equations, see [19 27].
The forward difference method discretizes the derivative operator by mapping whereas the backward difference method impose.
If then is the forward difference operator while is the backward difference operator.
where is the forward difference operator: and is the backward difference operator: ; and are real sequences.
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