طرق تكرارية موثوقة لحل معادلات فولتيرا التكاملية ضعيفة الانفراد الخطية وغير الخطية من النوع الثاني == Reliable Iterative Methods for Solving Linear and Nonlinear Weakly Singular Volterra Integral Equations of the Second Kind
Author name:
علي محمود شيحان علي
Supervisor name:
مجيد احمد ولي
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Baghdad
Language:
English
University location:
Baghdad
First pages:
27T1018 - p.pdf
Abstract:
The main aim of this thesis is solve weakly singular Volterra integral equations of the second kind of non - linear type in the form of a series with easily computable terms by using two methods. The first method is called the modified iterative method (DJM) which is proposed by Daftardar - Gejji and Jafari and the second is called the modified power series method (MPSM). Moreover, the comparison with an existing method such as Adomian decomposition method will be presented to demonstrate the efficiency of the proposed methods.Some examples will be solved to demonstrate that the presented methods are very effective, simple and does not require any restrictive assumptions.The first part of this thesis will discuss solving of weakly singular Volterra integral equations of the second kind and provide some definitions that we will be used later.The second part of this thesis deals with the implementation of the new iterative method namely (DJM) to solve the non - linear Volterra integral equations with weakly singular kernel of the second kind.In the third part, the recursive method namely the modified power series method (MPSM) is presented to solve the non - linear Volterra integral equations with weakly singular kernel of the second kind. Software to be learned and used in this thesis is MATHEMATICA.
