Download PDF by Edwin Zondervan: A numerical primer for the chemical engineer

By Edwin Zondervan

ISBN-10: 1482229447

ISBN-13: 9781482229448

"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. Read more...

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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.

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A numerical primer for the chemical engineer by Edwin Zondervan

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