Numerical Methods and MATLAB Techniques

In this book we shall use MATLAB codes and explain more involved features of MAT-LAB as we encounter them. MATLAB has a built-in help menu typing help format at the prompt, or help, for example, will show the syntax and variations of these two commands format and backslash . Whenever a student encounters a MATLAB command that is not self explanatory, we suggest using this built-in help function of MATLAB. 

There are many MATLAB tutorials available on the web please enter MATLAB tutorial into your favorite internet search engine (such as google, hotbot, infoseek, ly-cos, yahoo,. .., etc) and follow the offered links. Unfortunately, we cannot include a full fledged MATLAB tutorial in this book due to space and time concerns. 

This chapter continues with a description of a few basic numerical methods and their underlying principles. However, a solid first course in numerical analysis cannot be replaced by the concise intuitive explanations of numerical methods and phenomena that follow below. 

2 Numerical Methods and MATLAB Techniques for Chemical and Biological Engineering Problems 

In this section we give an overview of numerical analysis in general, and of the aspects of numerical analysis that are needed for problems encountered specifically in chemical and biological engineering2. This overview will, by necessity, be rather brief and it cannot substitute for a full semester course on Numerical Analysis. It is meant as a refresher only, or as a grain-of-salt type introduction to the theory and practice of mathematical computation. Many of the key terms that we introduce will remain only rather loosely defined due to space and time constraints. We hope that the unfamiliar reader will consult a numerical analysis textbook on the side see our Resources appendix at the end of the book for specific recommendations. This we recommend highly to anyone, teacher or student, who does not feel firm in the concepts of numerical analysis and in its fundamentals. 

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Contains mathematical methods including numerical methods and MATLAB Simulink techniques... 

Basically two search procedures for non-linear parameter estimation applications apply. (Nash and Walker-Smith, 1987). The first of these is derived from Newton s gradient method and numerous improvements on this method have been developed. The second method uses direct search techniques, one of which, the Nelder-Mead search algorithm, is derived from a simplex-like approach. Many of these methods are part of important mathematical computer-based program packages (e.g., IMSL, BMDP, MATLAB) or are available through other important mathematical program packages (e.g., IMSL). 

BROSIlow and Joseph Techniques of Model-based Control CONSTANTINIDES AND MoSTOUPl Numerical Methods for Chemical Engineers with MATLAB Applications... 

One of our main objectives in this primer is to demonstrate how to solve chemical engineering problems that require numerical methods by using standard algorithms, such as MATLAB or spreadsheets. To say it in simple words, it is to device and evaluate numerical techniques for employing computers to solve problems in chemical engineering. 

The above equations can be solved analytically to yield / for simple geometries such as a tube, an ellipse, and a rectangular channel with no sidewalls. For more complicated geometries such as a trapezoidal channel or one arising from isotropic etching fabrication methods, one has to resort to numerical solutions. In these cases, commercially available solvers such as FEMLAB and PDE Toolbox in MATLAB may be used to rapidly determine the dispersivity function/via numerical techniques. 

Numerical integration techniques are necessary in modeling and simulation of batch and bio processing. In this chapter we described error and stability criteria for numerical techniques. Various numerical techniques for solution of stiff and non-stiff problems are discussed. These methods include one-step and multi-step explicit methods for non-stiff and implicit methods for stiff systems, and orthogonal collocation method for ordinary as well as partial differential equations. These methods are an integral part of some of the packages like MATLAB. However, it is important to know the theory so that appropriate method for simulation can be chosen. 

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