Muhammad Aziz2016-05-212016-05-212016https://escholar.umt.edu.pk/handle/123456789/1981Supervised by: Dr. Muhammad Aziz ur RehmanIn this thesis our goal is to develop a third-order parallel splitting algorithm for solving linear partial di erential equation in two dimensions with non local boundary condition. In this method third-order approximations are used to approximate spatial derivative and Simpson's 1=3 rule is used to approximate the non local boundary condition. Using this Parallel algorithm the results of numerical experiments are examined, presented and compared with the exact solution, as well as with the results already existed in the literature and found to be highly accurate.MS ThesisHeat equationNonlocal boundary conditionThesis