Browsing by Author "Biset, Tesfa (PhD)"

Now showing 1 - 8 of 8
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    Analysis of Heat Equation in Rn
    (Addis Ababa University, 2020-06-16) Temesgen, Mehari; Biset, Tesfa (PhD)
    This paper is concerned with Analysis of heat equation in Rn. Analysis of heat equation in Rn regarded as Fourier Transformation which has di erent properties and Inverse of Fourier Transformation that is important to solve heat equation in 0n0 spaces. using separation of variables for solving with boundary conditions like Dirichlet, Neumann and periodic conditions. By using these condition we solve heat equations in Rn is solved.
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    Boundary Value Problems and Cauchy Problems For The Second-Order Euler Operator Differential Equation
    (Addis Ababa University, 2017-08) Adefris, Addisu; Biset, Tesfa (PhD)
    A differential equation is the most important part of mathematics for understanding many of the basic laws of physical sciences as well as other sciences. Some of the laws are formulated in terms of mathematical equations involving certain known and unknown quantities and their derivative. In this project paper we give a brief explicit solution of boundary-value problems and Cauchy problems for Euler operator differential equation and their reducibility are given in terms of solutions of algebraic operator equations
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    Harmonic Function and Partial Di erential Equations
    (Addis Ababa University, 2019-07-05) Debebe, Wubshet; Biset, Tesfa (PhD)
    This paper is concerned with harmonic function and partial di erential equation. Harmonic functions are regarded as solutions of Laplace equation which have a number of properties that are essential in solving partial di erential equation.Poisson integral is applied to obtain useful inequalities for positive harmonic functions.
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    Heat Equation and its Application in Homogeneous Dirichelt Boundary Condition
    (Addis Ababa University, 2018-09-01) Mekonnen, Bezuneh; Biset, Tesfa (PhD)
    In this paper, heat equation is derived using Fourier’s law of heat conduction and conservation of energy. In addition to this two laws Greens and divergence Theorem are used to change or transform line integral in to surface integral and volume integral in to surface integral respectively while deriving heat equation. The solution of heat equation is also investigated using separation of variables by considering homogenous Dirchelt boundary condition. The application of heat equation is also included.
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    Solving Second Order Pdes Using Fourier Transform
    (Addis Ababa University, 2019-07-03) Mekuria, Kassa; Biset, Tesfa (PhD)
    This project is concerned with the Fourier transform methods for second order partial di erential equations. In particular, solving wave, Laplace and heat equations using Fourier transform. We also introduce the theory of distributions and examine their relation to the Fourier transform, and we then use this methods to nd solutions to linear partial di erential equations. In particular, fundamental solutions to heat operators i
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    Sturm-Liouville and Periodic Sturm-Liouville Boundary Value Problems
    (Addis Ababa University, 2018-08-02) Negasi, Measho; Biset, Tesfa (PhD)
    In this project we discuss on, the eigenvalue problems that we have found so useful for solving the PDEs to a general class of boundary value problems that share a common set of properties. The so-called Sturm-Liouville problems define a class of eigenvalue problems, which include many of the previous problems as special cases. The S - L Problem helps to identify those assumptions that are needed to define an eigenvalue problem with the properties that we require.
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    Submitted in Partial Ful_Lment of the Requirement for the Degree of Master of Science in Mathematics
    (Addis Ababa University, 2019-05-30) Hailu, Tefera; Biset, Tesfa (PhD)
    This thesis is concerned with some Fundamental solution and Green's function for a System of second order and more, for Linear Elliptic partial di erential equations in two or more independent variables. Fundamental Solutions and a number of Green's Functions are given for cases when the coe cient in the equations are constant.
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    System of Non-Linear Ordinary Differential Equations and Stability Analysis
    (Addis Ababa University, 2018-09-01) Kebede, Brhane; Biset, Tesfa (PhD)
    The focus of this thesis is on the use of linearization techniques and linear differential equation theory to analyze nonlinear differential equations. Often, mathematical models of real-world phenomena are formulated in terms of systems of nonlinear differential equations, which may be difficult to solve explicitly. To overcome this barrier, we take a qualitative approach to the analysis of solutions to nonlinear systems by making phase portraits and using stability analysis. We demonstrate these techniques in the analysis of two systems of nonlinear differential equations. The first part of this paper gives a survey of standard linearization techniques in ordinary differential equation theory. The second part of the paper presents applications of these techniques to particular systems of nonlinear ordinary differential equation.