Faculty
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Year of Publication
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Publication Type
Abstract
Numerical methods for solving initial and boundary value problems play a crucial role in various fields of science and engineering.The objective of this project is to present a numerical iterative method for solving initial and boundary value problems to ordinary differential equations . This iterative method is based on the use of the Euler's method and the finite difference method (FDM) in solving initial and boundary value problems respectively. The project begins with a comprehensive literature review on numerical methods for solving IVPs and BVPs, emphasizing the theoretical foundations and practical applications of Euler's and
Finite difference methods. The mathematical formulations and algorithmic procedures of both methods are discussed in detail, highlighting their similarities, and differences. Furthermore, the Euler's method and the finite difference method enables us to approximate the solutions of an ordinary differential equation at a given initial value problem and boundary value problem respectively.
Indeed, two numerical examples are provided to illustrate the effectiv
ness of the Euler's and Finite difference methods. Results obtained show that the numerical method is very effective and convenient for solving ordinary differential equations with initial and boundary value
problems.
Finite difference methods. The mathematical formulations and algorithmic procedures of both methods are discussed in detail, highlighting their similarities, and differences. Furthermore, the Euler's method and the finite difference method enables us to approximate the solutions of an ordinary differential equation at a given initial value problem and boundary value problem respectively.
Indeed, two numerical examples are provided to illustrate the effectiv
ness of the Euler's and Finite difference methods. Results obtained show that the numerical method is very effective and convenient for solving ordinary differential equations with initial and boundary value
problems.
Supervisor(s)
co-supervisor