A Data Engineer working at Facilities of Futures Sdn. Bhd. The company is embracing the Fourth Industrial Revolution (IR 4.0). The company plans to design a long thin insulated metal rod from various types of metal for heat conduction. The engineer should consider three types of metal of length greater than 20 cm.

a) How to solve the temperature distribution by using two numerical methods for the three types of metal. What are the assumptions used to solve the problem.

b) Discuss any characteristics of the system of linear equations arising during solving the equations. Perform the simulation with various step sizes on both directions. Recommend on the type of metal that the company should use with justification inclusive of graph analysis.