Browsing by Author "Adefris Mamo"

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    On Poisson Equation and Green’s Functions in 2D
    (Addis Ababa University, 2024-09) Adefris Mamo; Tadesse Abdi
    This thesis explores the Poisson equation and its solutions through the application of Green’s functions in two dimensional domains. The Poisson equation, a fundamental partial differential equation in mathematical physics, describes the potential field generated by a given charge distribution. We begin by deriving the Green’s functions for the two dimensional Poisson equation emphasizing its role as a fundamental solution that encapsulates the boundary conditions & source terms. The thesis further investigates various methods for constructing Green’s functions including integral transforms and separations of variables, and demonstrate their application to specific boundary conditions. Additionally, we discuss the implications of our findings in physical context such as electrostatics and heat conduction. The results highlight the versatility and power of Green’s functions as a tool for solving linear differential equations, providing insights into theoretical aspects of the Poisson equation in two dimensions.