Mathematics

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Browsing Mathematics by Author "Abathun, Addisalem (PhD)"

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    Approximate Solution of Linear Differential Equation
    (Addis Ababa University, 2018-08-04) Aragaw, Getahun; Abathun, Addisalem (PhD)
    This thesis presents an efficient approach for determining approximate solutions of ordinary linear differential equations at ordinary points, near regular singular points and near irregular singular points. Test examples demonstrate the effectiveness and inefficiency of a given method at different points.
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    Euler's Method and Error Analysis
    (Addis Ababa University, 2018-08-12) Denekew, Tadfie; Abathun, Addisalem (PhD)
    In this paper we introduce the notion of Euler's method and error analysis. And we obtain various conditions for stability analysis and it has been shown that the Euler's method is convergent and consistent. The method is clari ed with the help of numerical illustration and graphical analysis.
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    On Subharmonic Functions and Potentials
    (Addis Ababa University, 2018-08-05) Feleke, Esubalew; Abathun, Addisalem (PhD)
    Potential Theory in the Complex Plane I’ll discuss some of the main definitions, theorems, and techniques on subharmonic functions and potential theory in the complex plane. This includes the origin of the subject in physics, connections with complex analysis, harmonic and subharmonic functions, logarithmic potentials, equilibrium potentials, Dirichlet problem, thin sets, polar sets, capacity.