Computer codes Matlab

Explicit equations are relatively straightforward to deal with — all that is required is to translate the equation into computer code, be it Matlab or Excel or any other language. 

For this example, we do not give the MATLAB code for the differential equations. The code can be fairly complex and, thus, its development is prone to error. The problem is even more critical in the spreadsheet application where several cells need to be rewritten for a new mechanism. We will address this problem later when we discuss the possibility of automatic generation of computer code based on traditional chemical equations. 

A Matlab computer code for the Hodgkin-Huxley model is given below. The code to compute the time derivatives of the state variables (the right-hand side of Equation (7.30)) is ... 

Matlab computer codes for the helix-coil model are given below. First, we introduce a function that computes and returns the vector [1, v, v, u2] M, given the inputs v, w, and k ... 

When writing a computer program, often it becomes necessary to execute a line or a block of yoiu-computer code many times. MATLAB provides and u>AiU commands for such situations. 

These solutions for the fractional uptake listed in Table 9.2-3 are used often in the literature, when linear isotherm is valid. The fractional uptake versus non-dimensional time T is shown in Figure 9.2-5a for three different shapes of the particle for the case of infinite stirring in the surrounding (Bi -> oo). The computer code UPTAKEP.M written in MatLab is provided with this book to help the reader to obtain the fractional uptake versus time. As seen in Figure 9.2-5a, for the given R and Dapp the spherical particle has the fastest dynamics as it has the highest exterior surface area per unit volume. 

They given the analysis of the local truncation error and the stability of all the methods mentioned above. For the local error truncation analysis the authors presented the relation between the error and the energy. The authors examined the accuracy and computational efficiency of all the above methods via the numerical approximation of five problems. Conclusions and open problems are also defined. Computational codes written in Maple are presented for the construction of all methods developed in this paper. Subroutines written in Matlab , for the application of the methods described are also presented. 

TAGS and MODELS are kinds of a compufer language by which a user can produce a computer code as an input data of fhe EMTP. Those are, in a sense, a pioneering software before MATLAB, MAPLE, and so on. If a user needs to develop a model circuit, which is not available in the EMTP, it can be achieved by using TAGS or MODELS. 

After the assembling of the stochastic matrix Pd we have to solve the associated non-selfadjoint eigenvalue problem. Our present numerical results have been computed using the code speig by Radke AND S0RENSEN in Matlab,... 

With the advent of modern software tools, however, tools such as MATLAB and even the older language, APL, matrix operations can be coded directly from the matrix-math expressions, and then it becomes near-trivial to create and solve the matrix equations on-the-fly, so to speak, and calculate the coefficients for any derivative using any desired polynomial, and computed over any odd number of data points. 

Initially, we develop Matlab code and Excel spreadsheets for relatively simple systems that have explicit analytical solutions. The main thrust of this chapter is the development of a toolbox of methods for modelling equilibrium and kinetic systems of any complexity. The computations are all iterative processes where, starting from initial guesses, the algorithms converge toward the correct solutions. Computations of this nature are beyond the limits of straightforward Excel calculations. Matlab, on the other hand, is ideally suited for these tasks, as most of them can be formulated as matrix operations. Many readers will be surprised at the simplicity and compactness of well-written Matlab functions that resolve equilibrium systems of any complexity. 

In order to solve chemical/biological problems of differing levels we rely throughout on well tested numerical procedures for which we include MATLAB codes and test files. Moreover, a large part of this book is dedicated to explain the workings of our algorithms on an intuitive level and thereby we give a valuable introduction to the world of scientific computation and numerical analysis. 

This chapter should be read and studied by our readers early on, with fingers on the keyboard of a computer, in order to gain a first working knowledge of MATLAB, and also later throughout the book as we introduce new numerical techniques and codes.]... 

If an item is entered in MATLAB without a designation such as x =. .. and is not followed by a , such an item will always be designated as ans on screen. This is short for answer . Such an object will be stored as ans in the workspace. Note that the contents of ans is freely and frequently overwritten. Please compare with the on-screen output of the first four size and length commands above that are comma delimited. If an item is named in MATLAB code, such as A, B, or result above are, it will carry that name throughout the computations (until reassigned) and be displayed on screen only if followed by a, or by a blank. 

MATLAB is a very simple language for computations. Its lines of numerical code are often few and short. By comparison, the visual output and the proper texting of graphs created in MATLAB may take much more effort than the numerics. 

This example gives a good overview of the kind of problems that chemical/biological engineers encounter daily with numerical computations. Besides, our numerical codes will introduce the reader to more advanced aspects of MATLAB programming and plotting. 

The last two codes contain many intricate and useful plotting and contour commands that are self-explanatory when one uses the MATLAB help. .. function for the MAT-LAB graphics commands meshgrid, surface, contour3, xlabel, ylabel, title, colormap, etc. Students should study these graphics commands of MATLAB in order to be learn how to display the easily computed numerical data well. Please refer to MATLAB help. ... 

We can validate our formulas and code against the earlier computed conversion rate of 72.64% at the end of the tubular reactor for the Damkohler number Da = 1.4 and Pe = 15.0 by running conversionDa(15,0.7264) with the inputs Pe = 15 and the conversion rate percent = 0.7264 (= xa) in MATLAB. This call computes the Damkohler number Da = 1.4007 correctly to within 0.05%. 

We start with a multi-density (or multi-colored on the computer screen) plot of six phase plots for the solution of (6.144) starting from various initial conditions. Each phase plot begins at a small o mark and ends at a specified time r = Tend at a small square. The plots in Figure 6.32 are generated by our MATLAB code threeCSTRrun.m which in turn relies on threeCSTR.m to solve each IVP of the form (6.144). 

We illustrate the theoretical concepts in a few selected computer programs and then apply them to realistic examples. MATLAB [5] is the programming language of choice for most chemometricians. The MATLAB code provided in the examples is intended to encourage and guide readers to write their own programs for their... 

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