I am trying to numerically solve the simple 2d heat equation (without any source and all the thermal properties assumed to be constant) using FVM. I am looking for a second-order accurate implicit time integration method. I have searched on the subject and most lectures talk about the first-order implicit Euler method or second-order explicit Runge Kutta method. I have tried understanding the second-order implicit Runge Kutta method but have found it very difficult to understand.
i) Is there a better second-order implicit method for my purpose? ii) Can someone please explain the implicit RK2 method?