الفهرس | Only 14 pages are availabe for public view |
Abstract Summary The object of this thesis which consists of ve chapters, is to study numerically by using CM and GM, the Appr. solutions, Min. error and Max. errors for FIEs, VIEs, F-VIE and V-FIE. At rst, in chapter one, we presented a general introduction. We focused on basic concepts and classication of IEs according to their kinds and kernels and how to convert BVBs and IVPs to IEs and vice versa. Also, we applied Picard’s method to discuss the existence and uniqueness of solutions for FIEs and VIEs. Finally, we presented some analytical methods for solving IEs. Chapter two was devoted to study the stability of error of some numerical methods for FIEs and VIEs. We concentrated our interest on using TR, SR, CM and GM. Also, we studied the behavior of errors at xed points in each case, investigating the Max. and Min. errors at each point and corresponding N of functions. Chapter three was concerned with the behavior of the Max. and Min. errors for F-VIE of the second kind using CM and GM. The Appr. solution was obtained by two techniques; the 1st TM depends on representing F-VIE as a system of FIEs of the second kind while the Appr. solution is obtained as functions of x at xed times. In the 2nd TM, we represented the Appr. solution as a sum of functions of x; t. Also, the comparisons between the results which werer obtained by two techniques in each method, were devoted. Results were represented in groups of gures and tables. ix Summary x Chapter four was focused on studying the behavior of Max. and Min. errors of solution for V-FIE by using CM and GM. Chapter ve was relevant to the applications of IEs in mathematical physics and mechanics. Therefore, there are some application which show how to convert a BVP or IVP to FIE or VIE |