Iterative method for solving a nonlinear fourth order boundary value problem

AbstractIn the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essence of the iteration is the simple iteration method for a nonlinear equation, although this is not shown in the papers of the authors.In this paper we propose a new approach to the solution of the problem, which is based on the reduction of it to finding a root of a nonlinear equation. In both cases, when the explicit form of this equation is found or not, the use of the Newton or Newton-type methods generate fast convergent iterative process for the original problem. The results of many numerical experiments confirm the efficiency of the proposed approach

The traditional portion of a Vietnamese colonial port city : commerce, politics, and the origin of Hải Phòng (1802-1888)

This article examines commercial activities, the impact of political interaction between the local powers and foreign colonialists, and other issues in the making of colonial port cities in Asia. By analyzing the formation history of Hải Phòng, one of largest seaports in Vietnam during the nineteenth century, the author of this study argues that indigenous factors played a more important role than other factors of the standard Western requirements for European powers to select places to establish ports in the early colonial period. Therefore, the convenience of an early modern trading center and the inland-connecting ability of Hải Phòng made it quickly become used as the main naval base in early expeditions of the French in Tonkin. Consequently, despite the difficulties of water transport to and from a seaport influenced by rivers and tides, the disagreement of scientist and the lack of infrastructure, the government of Indochina eventually decided to select Hải Phòng as the location to build the major port of northern Vietnam in the late nineteenth century. It is also the reason for this city not only maintaining marine exchange and transport under the domination of French colonialism but also remaining as an irreplaceable port in the northern part of modern Vietnam during the long twentieth century