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Browsing Mathematics by Author "Abdi, Tadesse (PhD)"
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Item Coexistence of Distributional and Rational Solution to Some Linear Ordinary Differential Equations(Addis Ababa University, 2016-03-21) Tadiyos, Gashawbeza; Abdi, Tadesse (PhD)In this paper, we visit a distributional solution of the di erential equation ty(n)(t) + my(n1)(t) + ty(t) = 0 where m and n are any integers with n 2 and t 2 R using Laplace transform technique. We nd that the types of Laplace transformable solution in the space of right-sided expiration depend on the relationship between m and n. Precisely, we have a distributional solution provided m n; and a weak solution otherwise.Item Explicit Finite Difference Scheme For 2d Parabolic Partial Differential Equation(Addis Ababa University, 2020-06-25) Negash, Habtemichael; Abdi, Tadesse (PhD)In this project report, explicit nite di erence scheme for 2D parabolic par- tial di erential equations is considered. This method is used to solve the partial derivatives in the partial di erential equations at each gride point that are de- rived from neighbouring values by using Taylors theorem. The forward-time centered-space(FTCS)and explicit schemes are developed. The MATLAB im- plementation allows to experiment with the stability limit of the forward-time centered-space(FTCS).Item Gradute Seminar Report on Fredholm Alternative Theorem and Higher Order Ordinary Differential Equations(Addis Ababa, 2010-06) Getaneh, Habtamu; Abdi, Tadesse (PhD)Item Multiplicity of Positive Solutions and the Method of Upper and Lower Solutions for Nonlinear Elliptic Pdes(Addis Ababa University, 2021-10-19) Mershaye, Dagmawit; Abdi, Tadesse (PhD)In this paper, we are interested in the positive solutions of nonlinear elliptic boundary value problems on a bounded domain. We establish the existence, uniqueness and multiplicity of positive solutions for the nonlinear elliptic boundary value problem of autonomous type, ( Lu = f (x, u) in W Bu = c(x) on ¶W and then proceed to establish conditions for existence and uniqueness of positive global solutions for the non-autonomous type elliptic BVP, 8>< >: ut 4u = f (x, t, u) in D Bu = c(x, t) on ¶D u(x, 0) = u0(x) in W We employ the method of lower and upper solutions along with the monotone iterative techniques to this end.Item Multiplicity of Positive Solutions of a Class of Ordinary Differential Equations With Nonlinear Boundary Conditions(Addis Ababa University, 2014-03-03) Kebede, Tesfahun; Abdi, Tadesse (PhD)In this paper we study the multiplicity solution of the boundary value problem u 00 + a(t)u 0 + f(u) = 0; B1(u(0)) u 0 (0) = 0; B2(u(b)) + u 0 (b) = 0; where 0 < t < b < 1, B1 and B2 2 C1[0;1); a 2 C[0;1) with a 0 on [0;1) and f 2 C[0;1) \ C1(0;1) satisfy suitable conditions. iiiItem On Duffing's Equation With Dirichlet Boundary Condition(Addis Ababa University, 2014-03-03) Tunshura, Aman; Abdi, Tadesse (PhD)We use a direct variational method in order to investigate the dependence on parameter for the solution of the following Du ng type equation with Dirichlet boundary conditions x (t) + r(t)x_ (t) Fx(t; x(t)) f(t) = 0 x(0) = x(1) = 0 and we observe that some outline of variational approach, in order to use this method.Item On Numerics of One Dimensional Advection Equation by Workye Gelaw(Addis Ababa University, 2020-07-04) Gelaw, Workye; Abdi, Tadesse (PhD)This project provides a practical overview of numerical solutions to the linear one dimensional Advection equation using finite difference method. It presents a number of schemes for solution of Linear Advection equation, which are based on the finite difference method, the finite element method and the method of characteristics. It also allow the reader to experiment with the consistency, stability and convergency of finite difference scheme for linear Advection equation and an example with working Matlab code for the scheme is presented. The aim of this project is to find an optimal and stable solution of a linear advection equation problems that can not be solved analytically easily on a given interval using finite difference methods.Item On the Fundamental Solution of Fractional Diffusion-Wave Equation(Addis Ababa University, 2021-04-29) Bekele, Abenezer; Abdi, Tadesse (PhD)In this thesis, explicit closed form for the fundamental solution of multidimensional space-time fractional diffusion-wave equation cDb t u + (4) a2 u = 0 with Cauchy data is considered. The Mellin transform is employed along with the Mellin-Barnes transform for specific values of a and b to achieve the representation of the fundamental solution in closed form.Item Seminar Report on: Positive Solution for Higher Order Nonlinear Eigen Value Problem(Addis Ababa University, 2007-07) Fikadu, Yared; Abdi, Tadesse (PhD)