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Item Third-order numerical method for the solution of heat equation with nonlocal boundary conditions(UMT Lahore, 2017) Kanwal TariqA third order numerical technique is developed for solving one dimensional non-homogenous heat equation with integral boundary conditions. In this method, second order spatial derivative is approximated by third order finite difference approximation. The parallel splitting technique combined with Simpson's 1/3 rule is used to tackle this problem. This method is very precise due to highly accurate results.Item Some properties of soft norm on soft linear space(UMT Lahore, 2017-06) GHULAM RASOOLIn this study, properties of soft norm on soft linear space have been studied. Some new properties of soft vector in soft linear space are introduced. A notion of soft linear space and soft norm on a soft linear space have been presented and some of their properties have been studied. Completeness of soft normed linear spaces, equivalent soft norms and convex soft sets are discussed and some of their properties are examined in soft normed linear space. The soft linear operator, soft continuous operator and their properties has been studied.Item Edge version of harmonic index and polynomial(UMT Lahore, 2017) Rabia NazirIn this thesis, we introduced the edge version of harmonic index and harmonic polynomial on the basis of the edges of a graph. Then we computed the edge version of harmonic index and polynomial for some standard classes of graphs. We also discussed some examples of rooted product graphs and bridge graphs in the context of harmonic index and polynomial.