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Item Modified forms of some convex polytopes with constant metric dimension(UMT Lahore, 2017) Sadia MehboobIn this thesis, we expand the study of metric dimension by adding r times pendant edges and adding r times prisms to the outer cycle of some convex polytopes determined in [21, 25]. These modified forms of convex polytopes have constant metric dimension, and only three appropriately chosen vertices are sufficient to resolve all the vertices of these graphs of convex polytopes.Item Convective flow of rotating MHD second grade fluid over an oscillating plate in a porous medium(UMT Lahore, 2017) Saba IramIn this research, the analytical solutions for unsteady free convection flow of rotating second grade fluid over an isothermal oscillating vertical plate are gained. The influence of magnetohydrodynamics (MHD) flow is also deliberated in a porous medium. The governing equation for momentum is sculpted in a rotating system such that both fluid and plate revolve in unison with uniform angular velocity. The phenomenon is sculpted in the froth of partial differential equation unruffled in the preliminary and boundary condition. Some appropriate non-dimensional variable are familiarized. The analogous non-dimensional momentum and energy equations with conditions are deciphered via Laplace transform technique. Expressions for velocity and temperature fields are found and demonstrated graphically for dissimilar values of second grade fluid, rotation, magnetic and porosity parameters. End result acquired gratified all the initial and boundary conditions.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 Fourth order numerical method for the solution of heat equation with nonlocal boundary condition(UMT Lahore, 2017-12-15) Anam ZahraIn this thesis, a numerical technique is developed for solving one-dimensional parabolic partial differential equation (PDE) with integral boundary conditions. The spatial derivative is approximated by a finite difference (FD) scheme, and by applying the method of lines, resulting in a system of ordinary differential equations (ODEs). Simpson’s 1/3 rule is used to tackle integral boundary conditions, and it also helps in removing additional variables to produce a system of N equations with N variables. This numerical method can be coded in sequential as well as parallel computing environments.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 3-total edge product cordial labeling of some standard classes of graphs and convex polytopes(UMT Lahore, 2017) Umer AliIn this thesis, our task is to study 3-total edge product cordial (3-TEPC) labeling of some standard classes of graphs and convex polytopes graphs. We discuss web graph, book graph, ower graph and some families of convex polytopes in the context of 3-TEPC labeling.Item Topological indices of line graphs of some convex polytopes and line graphs of their subdivisions(UMT Lahore, 2017) Fatima AsifIn this thesis, we give theoretical results for some topological indices such as geometric–arithmetic index GA(G), fifth geometric–arithmetic index GA5(G), atom–bond connectivity index ABC(G), fourth atom–bond connectivity index ABC4(G), Zagreb indices M1(G), M2(G), M3(G), M1(G), M2(G), Zagreb coindices M1(G), M2(G), M2(G), Randic index R(G), hyper-Zagreb index HM(G), general sum-connectivity index (G), and augmented Zagreb index AZI(G) by considering graph G as a line graph and line graph of the subdivision of some convex polytopes.Item Some standard classes of graphs labeled by 3-total edge product cordial labeling(UMT Lahore, 2017) Muhammad BilalOur task in this thesis is to study 3-total edge product cordial (3-TEPC) labeling of some standard classes of graphs. We discuss tadpole graph, helm graph, gear graph, banana tree graph, and recracker graph in the context of 3-TEPC labeling. We also discussed 3-TEPC labeling of some particular examples of graph operations like corona graphs.Item Soft Zorn’s lemma(UMT Lahore, 2017) FAIZ FARIDThe present research work is about Zorn’s lemma, fuzzy Zorn’s lemma, soft sets, and soft matrices. The research shows that the set of soft matrices and soft sets over the same universal set obey Zorn’s lemma.Item General solutions of convective flows of MHD Casson fluid with slip and radiative heat transfer at the boundary(UMT Lahore, 2017-04) Sana EjazThe purpose of this work is to find general solutions for magnetohydrodynamic (MHD) natural convection flow of an incompressible viscous fluid over an infinite vertical plate by considering radiative heat transfer, porous effects, and slip conditions. These solutions are obtained by the Laplace transform technique. They satisfy all imposed initial and boundary conditions and generate a large class of exact solutions. For illustration, three special cases are considered, and some interesting results from the literature are revived as limiting cases. The influence of different parameters on the fluid motion is graphically illustrated. This work has been published in the International Journal of Computational Thermal Sciences, Vol. 9, pp. 1–11 (2017).4Item Flow of natural convection near a perpendicular plate that applies a shear stress to a viscous fluid(UMT Lahore, 2017) Abida Ahmed KhanIn case of natural unsteady viscus fluid, the Laplace transformation method is used to study the stress of the fluid nearby a perpendicular plate. The heat of plate and shear stress is the reason for flow of fluid. By using Boussinesq approximation, closed form expression of temperature and velocity could be obtained. There are two special cases; also, fluid motion will be given in graphical form. In case of oscillating shear stress on boundary, time for the determination of steady state is also determined.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.Item Third order parallel splitting techniques for the solution of two dimensional heat equation with nonlocal boundary condition(UMT Lahore, 2017) Muhammad AzizIn this thesis our goal is to develop a third-order parallel splitting algorithm for solving linear partial differential equations in two dimensions with non-local boundary conditions. In this method, third-order approximations are used to approximate spatial derivatives, 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 existing in the literature, and found to be highly accurate.