Is there a program in which you "draw" a circuit indicating the voltage and current values in each part and the program returns the values of the capacitors, resistors, etc. to correspond to the voltage and current values?
Yes you could solve this problem assuming the math was accurate in both static and dynamic inputs, but , there is nothing that springs to mind more than just using Ohm's Law.
There isn't a mainstream program but there are circuit simulation tools like SPICE that allows you to simulate the behavior of electronic circuits based on the components and connections you define.
I recall back in the 80's along with our bed of nails ATE there were expensive options to reverse engineer PCB's to generate partial schematics of simple analog boards.