Read e-book online A numerical primer for the chemical engineer PDF

By Edwin Zondervan

ISBN-10: 1482229447

ISBN-13: 9781482229448

"This e-book emphasizes the deriviation and use of numerous numerical tools for fixing chemical engineering difficulties. The algorithms are used to unravel linear equations, nonlinear equations, usual differential equations and partial differential equations. it's also chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is followed because the programming setting through the book. Read more...

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You could prevent loss of digits, by first calculating e1 and subsequently calculating 1/(e ∗ e ∗ e ∗ e ∗ e). The Taylor series of e1 does not alternate, so loss of digits is prevented! 6 Ill-conditioned problems The introduction already mentioned is that errors in simulations can be traced back to 5 sources. 1. This type of error is called the propagated error. If the input x has a small error δx, then the output will be f (x+δx) instead of f (x). The propagated error is in this case f (x+δx)−f (x).

You could use the command lu. When we factorize matrix A into L, U , and P , we produce matrices that are less sparse than the original matrix. We have filled the elements between the offset and central band diagonals. 4 Contour plot of temperature profile >>subplot(1,2,2) >>spy(U) Doing Gaussian elimination on a matrix like A requires storage of more elements as the algorithm proceeds. If we had taken a 3D problem, we would have had another offset diagonal band, even farther from the central band.

1 Introduction In this chapter, we are going to write our first MATLAB program. This program can solve a set of linear equations. The method that we are going to use to perform the required row operations is called Gaussian elimination. But we will encounter some problems with Gaussian elimination, and for that reason we will resort to a decomposition technique called LU factorization. 2 MATLAB We already introduced MATLAB in the previous chapter as a user-friendly programming language. When you open the MATLAB user interface you will see a division of three screens: a work space, a command prompt, and a command history.

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A numerical primer for the chemical engineer by Edwin Zondervan

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