By Edwin Zondervan
"This ebook emphasizes the deriviation and use of quite a few numerical tools for fixing chemical engineering difficulties. The algorithms are used to resolve linear equations, nonlinear equations, traditional differential equations and partial differential equations. it is also chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is followed because the programming setting in the course of the book. MATLAB is a excessive functionality computing application. An introductory bankruptcy on MATLAB fundamentals has been extra and Excel clients can discover a bankruptcy at the implementation of numerical equipment in Excel. one other bankruptcy with labored out exaples are given within the Case examine bankruptcy to illustrate the numerical ideas. many of the examples have been written in MATLAB and have compatibility with the most recent types of MATLAB. you will need to point out that the most goal of this publication is to offer the scholars a style of numerical tools and challenge fixing, instead of to be a detailed advisor to numerical research. The chapters finish with small workouts that scholars can use to familiarize them selves with the numerical equipment. the fabric during this booklet has been utilized in undergraduate and graduate classes within the chemical engineering division of Eindhoven collage of expertise. to help teachers and scholars path fabrics have additionally been made to be had on the net at http://webpage.com. the writer may ultimately thank every body who has been valuable and supportive within the production of this publication, specially many of the Ph.D. scholars at Eindhoven college that experience assisted in the course of lectures and without delay inspired the content material of this e-book: Juan Pablo Gutierrez, Esayas Barega and Arend Dubbelboer"-- �Read more...
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Additional resources for A numerical primer for the chemical engineer
If you add a counter to the algorithm to monitor how many subtraction and multiplication operations are performed for a given size of matrix A, you will find that the number of operations for Gaussian elimination (row operations) is equal to the number of equations to the third power. For back substitution, the program requires a number of operations proportional to the square of the number of equations. Back substitution is more efficient than row operations, so maybe there are more efficient ways to end up with triangular matrices.
Explain the differences in CPU time. 1 Introduction We are going to take a look at iterative methods that can be used to solve large systems of (linear) equations. We will solve Laplace’s equation, which describes heat conduction in a rectangular geometry. 1) where α is the thermal diffusivity. ∇ is the partial derivative operator. We will consider this equation as a steady-state problem, with no dependence on time: α∇2 T = 0. 1 in two dimensions, for Cartesian coordinates we will have: ∂2T ∂2T + = 0.
5 Summary In this chapter we wrote a program that can solve a system of linear equations using Gaussian elimination and back substitution. This method is rather slow for large systems. MATLAB has a good solver of A\b itself. We found that back substitution is relatively fast and that repeatedly performing row operations slows down the solution process a lot. Decomposing a matrix into an L and a U matrix can be used to perform row operations systematically and much faster. The L and U matrices can directly be solved using forward and back substitution.
A numerical primer for the chemical engineer by Edwin Zondervan