عقيل الساعدي

This thesis develops various mathematical methods to acquire scientific study approximation solutions for time-fractional Burger’s equation. This thesis is divided into four chapters summarized as follows: Chapter One: The general introduction of Fractional calculus, spline function, and simplified illustration to the development and the analysis of numerical solutions to the fractional partial differential equations by referring to many authors who have redound expansion numerical analysis by using various Mathematical techniques. Chapter Two: Definitions and explanations of the in presented methods used such as Caputo time fractional derivative operator B-spline and explain Von Neumann method which will be used to investigate the stability of the numerical methods. Chapter Three: It includes an introduction to time-fractional Burger’s equation and its most important applications in various scientific issues, and then starts the process of finding numerical solutions to it using different mathematical methods such as Caputo time fractional derivative operator and several weighted residual methods using B-spline functions as a base function. The fractional derivative appearing in the time fractional Burger’s equation is approximated by means of the so-called L1 formulas and we derive several schemes to find solutions and prove that each one of them is unconditionally stable. Chapter four: A numerical example and results are given and compared the results of each scheme with others to show the best and most accurate method to find stable approximate solutions. Finally, the proposed methods were eva‎luated for accuracy and efficiency by using error norms 𝐿2 and 𝐿∞ and were compared to the previously mentioned numerical techniques.

معادله كسري - زماني برگر , روش عناصر متناهي بي - اسپلاين , پايداري

Time - Fractional Burgers Equation , B_ Spline finite Elements , stability

Aghil Alsaedi

Dr. Jalil Rashidi niya