This chapter is designed to help the user understand the concept of mathematical modeling to be able to utilize modeling in the development of their scientific applications research project. The most difficult part of modelling your project is being able to translate your problem into mathematical form. In order to effectively model a problem, you must understand what is involved in obtaining a solution. This involves being familiar with the variables, deciding what you expect in the way of results, and deciding upon a mathematical modeling approach.
Models vary significantly in their complexity and the types of answers they give.
You have to search out and decide what the right degree of complexity is for your particular problem. The start and end of a mathematical model is the real world situation. In a mathematical model we move from the real world to the abstract where we develop appropriate functions and equations. In this abstract world, we manipulate the functions and equations using mathematical techniques, often with the assistance of high power computational methods and high performance computers, such as supercomputers. Then we take the mathematical and computer solution back to the real world.