Explicit vs Implicit Techniques

The Forward Euler's method presents an elegant technique to march from time tn to tn+1 using the knowledge of the solution at time tn. Methods that allow marching from one time step to the next in such a fashion are referred to as Explicit methods. The right hand side of the equation for an Explicit method does not have any quantities from the left hand side.

On the other hand, methods such as the Backward Euler require iterations at each step to converge at a solution. Such methods that require an iterative solution are referred to as Implicit methods. In Implicit methods, both sides of the equation have a common variable, which is the one to be solved.