PSPICE simulation of capacitor voltage and current disagrees with math
How do you account for the switch in your hand calculations?

Spice has to do that. There is no such thing as a discontinuity when you are trying to do a continuous time simulation. Unless specialized algorithms are used, discontinuities require infinitesimally small time steps which require infinite time to simulate. For many algorithms this extends to discontinuities even in the derivatives.

Spice must be using some form of continuous model for the switch. Very likely a variable resistor that goes from very large to very small in a short amount of time. Faster than your 500nF capacitor time constant, but slower than your 500pF one.