Bir integro-diferensiyel denklem için başlangıç zaman farklı kuasilineerizasyon metodu

This thesis uses the Quasilinearization method to address an initial value problem involving a nonlinear integro-differential equation with initial time difference. By transforming the original equation into a sequence of linear differential equations and iteratively solving them, the method produces monotone sequences of lower and upper solutions that uniformly approaches to the unique solution. The impressive quadratic convergence of these sequences resulted in rapid reduction of approximation errors with each iteration. By performing appropriate computations, it has been successfully demonstrated that the sequences converge to the unique solution of the initial value problem. This achievement has significant implications, as it provides valuable insights into the complex behavior and properties of the nonlinear integro-differential equation with initial time difference. We expect that the study's findings will help us understand and solve some problems in science and engineering. The study is important in that it has new results and shows the effectiveness of the generalized quasilinearization method in solving integro-differential problems given with initial time difference.