تفاصيل الرسالة العلمية

In this thesis, the reproducing kernel method is applied for handling a class of system of ordinary differential equations, focusing interest on stiff problems. The solution philosophy depends on producing orthogonal basis from the acquired kernel function in the space W_2^2 [a,b]. The analytical and approximate solution are represented in the form of in convergent series with accurately computable structures in the space W_2^2 [a,b]. The n-term approximation is proved to converge uniformly to the analytical solution. The main features of the RKHS method lie in that it can be directly applied for solving nonlinear problems without the need for unphysical restrictive assumptions, such as linearization, discretization, perturbation, or guessing the initial data. Further, the numerical results are discussed by providing two illustrated examples. The gained results indicate that the proposed method is an attractive approximate technique for obtaining accurate outcomes to many problems occurring in natural sciences and physiscs