Do me a favor. I have some problem in simulation methods(Gear and Trapezoidal). When I run the circuit simulations in Multisim, It is normal to give a tips to change simulation integration method. But what the difference between the methods? And Where can I find the explanation of the methods.
the simulator extracts a set of differential equations from your netlist. Simulation actually means finding numerical solutions to those ODE-s. Gear and trapezoidal methods have to do with this numerical integration. There is lots of maths behind those. A search will give you more details on that math depending on the level you want to get into it.
From engineering and electrical simulation point of view, one or other method is used to help convergence. As a word of caution, trapezoidal integration can give fake numerical ringing in your simulations under certain conditions. Gear tends to artificially dampen real oscillations. In both cases you get bogus results.
Most simulators default to trapezoidal integration. Gear can be used to help convergence in switched mode systems with fast step voltages or currents and will typically be slower than trapezoidal. Gear should not be used for oscillator transient simulations because of the artifical damping.