Browsing by Author "Yesuf Jemal"

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    Asymptotic Solutions of Ordinary Differential Equations Having an Irregular Singular Point
    (Addis Ababa University, 2010-06-06) Yesuf Jemal; Abdi Tadesse (PhD)
    The problem of finding a basis solution of linear homogeneous ordinary differential equations with variable coefficients is, in general difficult. Indeed a considerable effort was directed at constructing solutions of specific equations with non constant coefficients. The solutions of differential equations with analytic coefficients were obtained from a theory called the method of power series. Most importantly is the case in which the equation has a singular point. In the special case of a so called regular (weak) singular point we can apply the method of Frobenius to construct convergent series solutions in a neighborhood of this point. In general this cannot be done for an irregular (strong) singular point. Treatment of this case is the main aim of this seminar. The first chapter gives the background information about the problem under investigated. The second chapter constructs a method of approximating the solutions of differential equations in a neighborhood of an irregular singular point. The final chapter extends these approximations to asymptotic expansions.