LTspice IV is a high performance SPICE simulator, schematic capture and waveform viewer with enhancements and models.
The simulator software can be downloaded from the following link:
As seen these switches are not a physical model, they require a initial voltage to start to act as one.
20150820_switch_RC is the simulation file for the given circuit, can be seen by installing LtSpice.
Every switch has some instance of resistance when on or off;
Ron = 1 ‘ the resistance when the switch is turned on.’
Roff = 10meg ‘ the resistance when the switch is turned off.’
Vt = 0.1 ‘ the instance when the switch turns on’
Classical way to solve the RC filter in time domain :