- #1

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[itex]\frac{dM}{dt}=4\pi \rho(r,t)r(t)^2\frac{dr}{dt}

[/itex]

which is the first term from

[itex]M(t)=4\pi\int_0^{r(t)}C(r,t)r(t)^2dr[/itex]

This describes the change in mass (M) of a sphere from a change in radius (r) given a density (rho) that depends on radius and time (t).

My problem is somewhat simple. I tried to convert this equation into a finite difference formula as follows:

[itex]M_1-M_0=4\pi \rho(r,t)r^2(r_1-r_0)[/itex]

where subscript 1 indicates the value at a new timestep.

I must be doing something wrong because the volume of a sphere requires a 1/3 to come from somewhere on the right hand side..