A numerical primer for the chemical engineer by Edwin Zondervan

By Edwin Zondervan

"This e-book emphasizes the deriviation and use of a number of numerical equipment for fixing chemical engineering difficulties. The algorithms are used to resolve linear equations, nonlinear equations, traditional differential equations and partial differential equations. additionally it is 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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10) where σ is the sign of x (positive or negative) and ci (i = 1, 2, 3, · · · , m) can have the value 0 or 1. The exponent e is always an integer. The part between brackets is called the mantissa. Notice that c1 is always 1. We have to choose the exponent e in such a way that the first nonzero digit corresponds to 2e−1 . The total number of available positions, λ + 1, has to be divided: the sign requires one position, the mantissa requires m − 1 positions, so the exponent has only λ−m+1 positions.

The matrix produced by elimination takes up a lot of memory. But for MATLAB, this is not a problem (it allocates extra memory). MATLAB also reorders the equations so that elements are moved closer to the diagonal. 4 Iterative methods In conclusion, Gaussian elimination is not ideal for solving sparse systems. 5 With LU decomposition, we produce matrices that are less sparse than the original matrix methods. In the early days of computing, iterative methods were important because memory was limited.

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. The matrix produced by elimination takes up a lot of memory. But for MATLAB, this is not a problem (it allocates extra memory). MATLAB also reorders the equations so that elements are moved closer to the diagonal. 4 Iterative methods In conclusion, Gaussian elimination is not ideal for solving sparse systems.

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