Browsing by Author "Icon Abebe"

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    Sturm-Liouville Boundary Value Problems and General Solutions to 2D Liouville Equations
    (Addis Ababa University, 2024-07-24) Icon Abebe; Tesfa Biset
    The thesis focuses on Sturm-Liouville equations, boundary value problems, and the general solutions to 2D Liouville Equations. It covers computations of eigenvalues and eigenfunctions, types of Sturm-Liouville boundary value problems, solving methods and solutions, inner products of eigenfunctions, and orthogonality of eigenfunctions with weighted functions. It also covers applications of Strum-Liouville Boundary Value problems and ways to solve them. Additionally, the thesis covers several characteristics of complex-valued functions and derivations emphasizing the significance of the Liouville Equation in resolving Elliptic as well as Hyperbolic 2D differential equations. Furthermore, it provides a short but detailed analysis aimed at enhancing the understanding and application of SLP, even at its most complex levels in science and engineering, thereby promoting general solution techniques for elaborate mathematical problems.