Chapter 27, Problem 24P

Solve the nondimensionalized ODE using finite difference methods that describe the temperature distribution in a circular rod with internal heat source S

$\frac{d^{2}T}{d{r}^2}+\frac{1}{r}\frac{dT}{dr}+S=0$

over the range $0\le r\le 1$, with the boundary conditions

$T\left(r=1\right)=1{\frac{dT}{dr}|}_{r=0}=0$

for $S=1,{\text{ 10, and 20 K/m}}^2$. Plot the temperature versus radius.