 Welcome back MechanicalEI, did you know that Crank Nicholson method was used for numerically solving the heat equation by John Crank and Phyllis Nicholson? This makes us wonder, what is Crank Nicholson method? Before we jump in, check out the previous part of this series to learn about what partial differential equations are. Now, due to some limitations over explicit scheme, mainly regarding convergence and stability, the schemes were developed which have less truncation errors and are conventionally convergent and stable. Similar to Bender-Schmidt formula, there is Crank Nicholson implicit method and is given as shown here. It converges on all values of lambda. When lambda equals to 1 that is k equals to a h square, the simplest form of the formula is given by value of a which is average of the values of u at b, c, d and e. This method, the values of u at a time step are obtained by solving a system of linear equations in the unknowns u and i. The last method is a successive over relaxation or SOR method given a square system of n linear equations with unknown x such that ax equals to b where a, x and b are denoted by the following matrices. And a can be decomposed into diagonal component d strictly lower and upper triangular components l and u such that a equals to the sum of dl and u. The system of linear equations may be written as d plus omega l into x equals to wb minus omega u plus omega minus 1 into d into x for a constant omega greater than 1 called the relaxation factor. The method of successive over relaxation is an iterative technique that solves the left hand side of this expression for x using previous value of x on the right hand side. Analytically, this will be written as x power k plus 1 equals to the product of l omega and x power k plus c, here x power k denotes the kth approximation or iteration of x. Hence, we first saw what Crank Nicholson method is and then went on to see what successive over relaxation method is. So like, subscribe and comment with your feedback to help us make better videos. Thanks for watching.