Difference between revisions of "NumericalDiffEqs"

From Sean_Carver
Jump to: navigation, search
Line 10: Line 10:
  
 
<math> \frac{dy}{dt} = - k y </math>
 
<math> \frac{dy}{dt} = - k y </math>
 +
 +
Here k is the rate constant, 1/k is the time constant, 1/k is <math> \frac{C}{g_L} = RC </math> in the notation above.  The bigger k the higher the rate of convergence, and the smaller the time constant 1/k.  The time constant is the time it takes the solution to decay to 1/e of its value.
  
 
Click here for [[Media:intuit.hoc|code]] for visualizing the numerical solution of differential equations.
 
Click here for [[Media:intuit.hoc|code]] for visualizing the numerical solution of differential equations.

Revision as of 22:35, 12 February 2009

Remember the equation for the cell with only leak channels.

 C \frac{dV}{dt} = I(t) - g_L(V - E_L)

Let's simplify: suppose there is no injected current and that the reversal potential for the leak channels is  E_L = 0 . Then our equation is

 \frac{dV}{dt} = - \frac{g_L}{C} V

Using different letters for the variables (because this is done in the software linked below):

 \frac{dy}{dt} = - k y

Here k is the rate constant, 1/k is the time constant, 1/k is  \frac{C}{g_L} = RC in the notation above. The bigger k the higher the rate of convergence, and the smaller the time constant 1/k. The time constant is the time it takes the solution to decay to 1/e of its value.

Click here for code for visualizing the numerical solution of differential equations.