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Tweaked spelling in title, fixed split infinitive.
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Geoff Oxberry
Geoff Oxberry
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Can I use an explict timestepingexplicit time stepping scheme to numerically determine numerically whether an ODE is stiff?

I have an ODE:

$u'=-1000u+sin(t)$
$u(0)=-\frac{1}{1000001}$

I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (eulerEuler, rungeRunge-kuttaKutta, adamsAdams, etc.), the method should return very large errors if the time step is too large. So, I have two questions:

  1. Is this how stiff ode'sODEs are determined, in general, when an analytical expression for the error term is not available or derivable?

  2. In general, when the odeODE is stiff, how do I determine a "small-enough" enough" timestep?

Can I use an explict timesteping scheme to numerically determine whether an ODE is stiff?

I have an ODE:

$u'=-1000u+sin(t)$
$u(0)=-\frac{1}{1000001}$

I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (euler, runge-kutta, adams, etc.), the method should return very large errors if the time step is too large. So, I have two questions:

  1. Is this how stiff ode's are determined, in general, when an analytical expression for the error term is not available or derivable?

  2. In general, when the ode is stiff, how do I determine a "small-enough" timestep?

Can I use an explicit time stepping scheme to determine numerically whether an ODE is stiff?

I have an ODE:

$u'=-1000u+sin(t)$
$u(0)=-\frac{1}{1000001}$

I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (Euler, Runge-Kutta, Adams, etc.), the method should return very large errors if the time step is too large. So, I have two questions:

  1. Is this how stiff ODEs are determined, in general, when an analytical expression for the error term is not available or derivable?

  2. In general, when the ODE is stiff, how do I determine a "small enough" timestep?

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Paul
Paul
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  • 8
  • 59
  • 132

Can I use an explict timesteping scheme to numerically determine whether an ODE is stiff?

I have an ODE:

$u'=-1000u+sin(t)$
$u(0)=-\frac{1}{1000001}$

I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (euler, runge-kutta, adams, etc.), the method should return very large errors if the time step is too large. So, I have two questions:

  1. Is this how stiff ode's are determined, in general, when an analytical expression for the error term is not available or derivable?

  2. In general, when the ode is stiff, how do I determine a "small-enough" timestep?