A high order numerical method for solving partial differential equations and its applications in Financial Mathematics and Computational Biology Highly Accurate Compact Finite Difference Method and its Applications.

The first argument is that software development should be based on scientific manners, and so should employ procedures similar to scientific methods. The flaw of this argument is the assumption that there is such a thing as scientific method and that it is helpful to scientists. This question has been the subject of much debate in recent years, and the conclusion of such authors as Feyerabend [1978], taking his illustrations from the history of physics, and Medawar [1982], arguing as a biologist, is that the notion of scientific method as a set of guidelines for the practising scientist is mistaken. This conclusion is not contradicted by such work as that of Polya [1954, 1957] on problem solving. This work takes its illustrations from the field of mathematics and leads to insight which is also highly relevant to programming. However, it cannot be claimed to present a method on which to proceed. Rather, it is a collection of suggestions aiming at stimulating the mental activity of the problem solver, by pointing out different modes of work that may be applied in sequence ...»