Error with Numerical Solution of PDE

Questions
1

I have the following code

Needs["DifferentialEquations 'InterpolatingFunctionAnatomy ’ ]

pde = D[C[x, t], t] == D[C[x, t], x, x] - (1.5*C[x, t])/(.01 + C[x, t])

soln = NDSolve[{pde, C[x, 0] == 0,
C[0, t] == if[0 < t <= 10, .0089, 0],
C[.01, t] == if[0 < t <= 10, 6658.125, 0]},
C, {x, 0, .01}, {t, 0, 1}]

with the following output:

NDSolve::ibcinc: Warning: boundary and initial conditions are inconsistent. >>

NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`. >>

Can somebody explain this error to me?

2

Your equation is nonlinear. Perhaps NDSolve for PDE is only designed for linear equations, at the moment.

3

You wrote “if”.

The function is “If”. Built in symbols are always capitalized.

The error message is complaining that initial conditions don’t make sense. This is because you are using “if” instead of “If”.