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An Efficient Method For Solving Singularly Perturbed Two Points Fractional Boundary-Value Problems, Suha Atallah Abdelhadi
An Efficient Method For Solving Singularly Perturbed Two Points Fractional Boundary-Value Problems, Suha Atallah Abdelhadi
Theses
In this thesis, we present numerical method for approximating the solutions of singularly perturbed two points boundary value problems in both cases: ordinary derivatives and fractional derivatives. We use the Caputo derivation for the fractional case. The method starts with solving the reduced problem then the boundary layer correction problem. A series method; namely, the Adomian decomposition method is used to solve the boundary layer correction problem, and then the series solution is approximated by the , - Pade’ approximation of order. Numerical and theoretical results are presented to show the efficiency of the method. Singularly perturbed problems arise frequently …
Solving Nonlinear Boundary Value Problems Using The Homotopy Analysis Method, Ghada Ayed Janem Ayed Janem
Solving Nonlinear Boundary Value Problems Using The Homotopy Analysis Method, Ghada Ayed Janem Ayed Janem
Theses
Analytical solutions of differential equations are very important for all researchers from different discipline. Obtaining such solutions is difficult in most cases, especially if the differential equation is nonlinear. One of the mostly used methods are the series methods, where the solution is represented as an infinite series. Different methods are available to evaluate the terms of this series. These methods include the well-known Taylor series method, the Adomian decomposition method, the Homotopy iteration method, and the Homotopy analysis method. In this thesis we give a survey of the different series methods available to solve initial and boundary value problems. …