M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Studies On Inner Product Spaces And Hilbert Spaces(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Laraib Akram; SP23-RMT-013; Dr. Kashif Nazar; LHR TP 9578Studies On Inner Product Spaces And Hilbert SpacesItem Integral Equations Method for Ahlfors Map and its Zeros(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Muhammad Ilyas; SP19-RMT-023; LHR TP 7409; Dr. Kashif NazarThe purposeofthisstudyistoexamineandanalyzetheboundaryintegral equations ofanAhlforsmapformultiplyconnectedregions.Alsotoderive some newboundaryintegralequationsrelatedtoanAhlforsmapwhich maymorebesuitableforfindingtheAhlforsmapanditsunknownzeros. The Nystr¨om methodwiththetrapezoidalrulewillbeusedtoparametrize and discretizetheseintegralequationsintosystemsofequations.Item Formation and Analysis of Ahlfors Map Integral Equations for the Regions with Multiple(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Usman Ashraf; Sp19-RMT-005; LHR TP 7410; Dr. Kashif NazarThis research work elaborates the detailed numerical analysis of the integr equation related to Szegö kernel and Ahlfors map with the assistance Mathematica 12.0. The Ahlfors map and Szegö kernel are both associated to ea other. This is a Fredholm integral equation of second kind via Kerzman-Stein kern where Szegö kernel is the solution of this integral equation. The solution of integr equation is obtained by transforming the integral equations into matrix form aft discretizing. This work presents the computation techniques of Ahlfors map, zeros, boundary values and the interior points of a region under Ahlfors map. Th research construct one new Ahlfors map integral equation with Neumann-ty kernel for the regions with multiple connectivity onto a unit disk. The kernel an non-homogeneous term of this equation contain zeros of Ahlfors map. This integr equations is constructed by a non-homogeneous boundary relationship for t regions with multiple connectivity. The new Ahlfors map integral equation analyzed by parameterizing and discretizing. Discretized integral equations leadItem Analyzing the Nystrom Method for Second Kind Fredholm Integral Equations(Library Information Services COMSATS University Islamabad Lahore Campus, 2023-03-12) Kainat Tahir; SP22-RMT-017; LHR TP 8724; Dr. Kashif NazarThis research proposal aims to study if second-kind Fredholm Integral Equations can possibly be solved using the Nystrom Method, which are common in many different fields and which require for the development of effective numerical solutions. The Nystrom Method will be thoroughly examined, along with an explanation of how it applies to second-kind Fredholm Integral Equations. Additionally, it will look at how different parameters influence the convergence of the Nystrom Method, such as the number of discretization points and the choice of numerical quadrature. The expected outcomes are meant to deepen our understanding and facilitate the advancement of numerical algorithms, leading to a more reliable and efficient solutions for integral equations. This discovery holds importance for numerous scientific and engineering domains, and it can lead in advancements in computer methodologies