Efficient strategies for solving nonlinear problems in BVPs codes

Abstract

Almost all the difficult mathematical problems arising in the applications are solved numerically. This is especially true for large size linear problems and for nonlinear ones. The main tools for the numerical treatment of problems on computers are appropriate codes which are highly sophisticated programs, able to solve specific classes of mathematical problems by only providing the essential data required by the problem itself. This last assertion implies that the user, often, needs not to know about the logical difficulties and the procedures which the codes are based on: the user is often required to do a little more than to push a button. Nevertheless, the role of numerical codes in the development of technology is a fundamental one. The main scope of this review paper is to give an idea of what is inside the codes and and to give an overview of the state of art not of the whole discipline, which is enormous, but only of the part of it concerning the codes for the solution of differential problems.