Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 193169 19 pages doi 2009 193169 Research Article Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions Ahmed Alsaedi and Bashir Ahmad Department of Mathematics Faculty of Science King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Ahmed Alsaedi aalsaedi@ Received 16 November 2008 Accepted 14 January 2009 Recommended by Yong Zhou A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order k k 2 for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits. Copyright 2009 A. Alsaedi and B. Ahmad. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Vascular diseases such as atherosclerosis and aneurysms are becoming frequent disorders in the industrialized world due to sedentary way of life and rich food. Causing more deaths than cancer cardiovascular diseases are the leading cause of death in the world. In recent years computational fluid dynamics CFD techniques have been used increasingly by researchers seeking to understand vascular hemodynamics. CFD methods possess the potential to augment the data obtained from in vitro methods by providing a complete characterization of hemodynamic conditions blood velocity and pressure as a function of space and time under precisely .
