pazdzioch

08-20-2007, 04:11 AM

Dear Granville,

in order to find a time step suitable for my computations I decided to observe the fastest process appearing in the model I use, namely Alfven waves in plasma physics. The equations, after some derivation may be rewritten in a form of one, wave equation with an analytical solution - simple oscillation has been obtained. The problem now is in the case of numerical computation the amplitude of the oscillation is decaying. I have found out that it happens mainly because of backward Euler scheme. In the case of Crank-Nicolson method the oscillation does not decay. Could you explain it shortly? The most important question is related to a more complex system - is this fast oscillation process damped always then when using the Euler scheme? Is there a difference in efficiency between both methods?

Thank you very much,

Dominik

in order to find a time step suitable for my computations I decided to observe the fastest process appearing in the model I use, namely Alfven waves in plasma physics. The equations, after some derivation may be rewritten in a form of one, wave equation with an analytical solution - simple oscillation has been obtained. The problem now is in the case of numerical computation the amplitude of the oscillation is decaying. I have found out that it happens mainly because of backward Euler scheme. In the case of Crank-Nicolson method the oscillation does not decay. Could you explain it shortly? The most important question is related to a more complex system - is this fast oscillation process damped always then when using the Euler scheme? Is there a difference in efficiency between both methods?

Thank you very much,

Dominik