https://repository.ju.edu.et//handle/123456789/139 Sun, 05 Apr 2026 22:09:46 GMT 2026-04-05T22:09:46Z https://repository.ju.edu.et//handle/123456789/10227 Quadratic B-spline Collocation Method for Solving Singularly Perturbed Quasilinear Sobolev Equations Lemessa Fikadu Babe; Gemechis File; Feyisa Edosa In this thesis, the one-dimensional singularly perturbed quasilinear Sobolev equationis considered and treated numerically. Newton’s linearization approach is used to linearize the nonlinear term. The finite difference method is used to treat the linearized equation spatial direction discretization. The temporal direction the quadratic B-spline collocation method is applied. The propsed scheme’s stability is analysed and established. The scheme converges with an order of convergence one in time and two in space. The theoretical results were illustrated using numerical example. Sun, 22 Dec 2024 00:00:00 GMT https://repository.ju.edu.et//handle/123456789/10227 2024-12-22T00:00:00Z https://repository.ju.edu.et//handle/123456789/10187 Non-Standard finite difference scheme based on the ta-Method For predator-Prey dynamical system Issa Zakir Abagidi; Woinshet Defar Mergia; Mebratu Fenta Wakeni In this thesis, a Non-Standard Finite Difference (NSFD) method based on the θ− method is formulated for solving the mathematical model of the Beddington-DeAngelis functional response predator-prey dynamical system. The NSFD scheme incorporates a time step function, which ensures the preservation of key qualitative features of the continuous system while providing flexibility in handling stiffness. A rigorous linear stability and convergence analysis is conducted to evaluate the scheme’s theoretical properties. This analysis exhibits the advantages of the NSFD method in preserving stability, accuracy, and convergence, making it a robust tool for modeling ecological and dynamical systems. Numerical comparisons between the proposed method and existing methods demonstrate that the new NSFD-based approach exhibits superior accuracy and convergence Tue, 18 Mar 2025 00:00:00 GMT https://repository.ju.edu.et//handle/123456789/10187 2025-03-18T00:00:00Z https://repository.ju.edu.et//handle/123456789/10036 An Iterative Algorithm for a Common Solution of Split Equality of Variational Inequality Problem of Pseudomonotone Mappings in Banach Spaces Tesfaye Etana Amante; Getahun Bekele; Mafuz Humer In this thesis we introduced an iterative algorithm for a common solution of split equality of variational inequality problem of pseudomonotone mappings in Ba nach spaces and proved a strong convergence of a sequence generated by proposed algorithm to asolution of split equality of variational inequality problem of pseu domonotone mappings in Banach spaces. Finally, we gave applications of our main results to approximate a common solution of split equality minimum point prob lem for convex functions in real re exive Banach spaces. Our results extended and generalized many results in the literature. Fri, 27 Dec 2024 00:00:00 GMT https://repository.ju.edu.et//handle/123456789/10036 2024-12-27T00:00:00Z https://repository.ju.edu.et//handle/123456789/10031 Cubic Non-Polynomial Spline on Piecewise Mesh for Robin Type Singularly Perturbed Reaction Diffusion Problem Bethelhem Esayas Ayele; Tesfaye Aga Bullo; Gemechis File Duressa This thesis introduces a novel approach to solving Robin type singularly perturbed reaction diffusion problems through cubic non-polynomial spline approximation on a piecewise mesh. The methodology involves discretizing the solution domain using a piecewise mesh size, followed by defining a cubic non-polynomial spline function and obtaining its derivatives. Subsequently, the derivatives in the differential equations are transformed into difference approximations, leading to a linear system of algebraic equations expressed in a three-term recurrence relation, solvable through an elimination algorithm. The stability and consistency of the method are thoroughly investigated to ensure its convergence. Furthermore, numerical model examples are employed to validate the proposed method, with results compared against other methods cited in the literature. The maximum absolute error and order of convergence for each model example are presented to demonstrate the significant advancements offered by the present method. Tue, 11 Jun 2024 00:00:00 GMT https://repository.ju.edu.et//handle/123456789/10031 2024-06-11T00:00:00Z