Difference between revisions of "NumericalDiffEqs"
From Sean_Carver
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<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.
Let's simplify: suppose there is no injected current and that the reversal potential for the leak channels is 
. Then our equation is
Using different letters for the variables (because this is done in the software linked below):
Here k is the rate constant, 1/k is the time constant, 1/k is 
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.
