ode-solver - iteration scheme?
in [Matlab]
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From: Manuel on 22 Mar 2010 08:43 I have a linear equation of motion, for a flapped airfoil with damper and springs. M*ddx + D*dx + C*x = F(t,x,dx) The calculation of the aerodynamic forces is performed through a panel-method based on Hess and Smith. The solution is obtained using the ode45-solver, which seems to give accurate results. My question is, does the ode-solver take in account the dependency of displacement x and the velocity dx of the flaps properly? MATLAB calculates the forces at the beginning of every time-step, but they change during the time-step. Isn't there an iteration scheme like any kind of predictor-corrector-method necessary? Thank you in anticipation!
From: Bruno Luong on 22 Mar 2010 09:10 "Manuel " <manuel.jain(a)gmx.net> wrote in message <ho7okm$cbt$1(a)fred.mathworks.com>... > I have a linear equation of motion, for a flapped airfoil with damper and springs. > > M*ddx + D*dx + C*x = F(t,x,dx) > > The calculation of the aerodynamic forces is performed through a panel-method based on Hess and Smith. The solution is obtained using the ode45-solver, which seems to give accurate results. > My question is, does the ode-solver take in account the dependency of displacement x and the velocity dx of the flaps properly? MATLAB calculates the forces at the beginning of every time-step, but they change during the time-step. Isn't there an iteration scheme like any kind of predictor-corrector-method necessary? Huh? It is *your* responsibility to program the dependency. The runge-kutta scheme (ode45) *is* a predictor-corrector method. Bruno
From: Manuel on 22 Mar 2010 09:57 Dear Bruno, Thank you for your fast reply. The calculation of the forces is correct. But if you look at the first time-step, the ode-solver accesses the force calculation and then integrates the equation of motion. The magnitude of the force changes during the time-step. For instance, ode starts at t_0 and calculates F, integrates the equation and reaches time-step t_1 = t_0 + h, with h being the step-size. The magnitude of F at time, let's say, t = t_0 + h/2, is different, due to the displacement x, but the integration is based on F(t_0,x_0,dx_0). So does ode take care of this inexactness? Regards.
From: Bjorn Gustavsson on 22 Mar 2010 11:36 "Manuel " <manuel.jain(a)gmx.net> wrote in message <ho7svf$1nk$1(a)fred.mathworks.com>... > Dear Bruno, > Thank you for your fast reply. > The calculation of the forces is correct. But if you look at the first time-step, the ode-solver accesses the force calculation and then integrates the equation of motion. The magnitude of the force changes during the time-step. For instance, ode starts at t_0 and calculates F, integrates the equation and reaches time-step t_1 = t_0 + h, with h being the step-size. The magnitude of F at time, let's say, t = t_0 + h/2, is different, due to the displacement x, but the integration is based on F(t_0,x_0,dx_0). So does ode take care of this inexactness? > Regards. To make good use of matlab you need to learn to use help. At the matlab prompt type: help then: help ode45 If you don't find the information you're wondering about you have to look in the documentation, type: doc ode45 HTH, Bjeorn
From: Torsten Hennig on 22 Mar 2010 06:21
> I have a linear equation of motion, for a flapped > airfoil with damper and springs. > > M*ddx + D*dx + C*x = F(t,x,dx) > > The calculation of the aerodynamic forces is > performed through a panel-method based on Hess and > Smith. The solution is obtained using the > ode45-solver, which seems to give accurate results. > My question is, does the ode-solver take in account > the dependency of displacement x and the velocity dx > of the flaps properly? MATLAB calculates the forces > at the beginning of every time-step, but they change > during the time-step. Isn't there an iteration scheme > like any kind of predictor-corrector-method > necessary? > > Thank you in anticipation! The fact that ODE45 is an explicit integrator does not cause that the results are less accurate than those obtained by an implicit solver. The only advantage of implicit solvers is that they can better cope with stiff problems. If you notice that ODE45 makes very small time steps, you should switch to such an implicit integrator. Best wishes Torsten. |