Department of Mathematics

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Author: search.filters.author.Dr. Kashif NazarSubject: search.filters.subject.Mathematics

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Now showing 1 - 5 of 5
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    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 9578
    Studies On Inner Product Spaces And Hilbert Spaces
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    Analysis of the Formulations and Continuities of Kernels of Integral Equations for Ahlfors Map
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Muhammad Amin Khan; FA22-RMT-017; Dr. Kashif Nazar; LHR TP 9380
    This study aims to examine and analyze the boundary integral equations of the Ahlfors map specifically for multiply connected regions. The Ahlfors map, known for mapping the boundary of a domain to the unit circle, helps in understanding the domain’s structure. Our goal is to rederive boundary integral equations that are more effective in determining the Ahlfors map and its unknown zeros. Identifying these zeros is crucial as they provide important information about the map’s behavior and the domain’s geometry. By develop ing these new equations, we hope to address existing challenges and solve long-standing problems in the field, ultimately advancing mathematical understanding and applications of the Ahlfors map in complex analysis and related disciplines.
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    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 Nazar
    The purposeofthisstudyistoexamineandanalyzetheboundaryintegral equations ofanAhlforsmapformultiplyconnectedregions.Alsotoderive some newboundaryintegralequationsrelatedtoanAhlforsmapwhich maymorebesuitableforfindingtheAhlforsmapanditsunknownzeros. The Nystr¨om methodwiththetrapezoidalrulewillbeusedtoparametrize and discretizetheseintegralequationsintosystemsofequations.
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    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 Nazar
    This 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
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    Discussions on Solutions of Fredholm Integral Equations
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Muhammad Adeel Khan; CIIT/SP21-BSM-022/LHR; Dr. Kashif Nazar; LHR TP 9888
    This thesis investigates the analytical and numerical solutions of Fredholm integral equa- tions of the second kind, focusing on both homogeneous and non-homogeneous cases. In the analytical framework, we explore solutions with degenerate kernels and methods to ap- proximate complex kernels by degenerate forms, providing efficient pathways for problem simplification. The study covers both theoretical and applied aspects, emphasizing cases where the kernel exhibits specific structures that facilitate closed-form solutions. Numer- ical methods are also developed and analyzed for solving these integral equations in both homogeneous and non-homogeneous settings. The numerical approaches are evaluated for their accuracy and computational efficiency, providing insights into practical implemen- tations and approximations for real-world applications. Through comprehensive analysis and comparison of methods, this research contributes to the effective solution of Fredholm integral equations, offering new perspectives for both theoretical exploration and applied problem-solving.