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Numerical Methods for Engineers and Scientists

Lecturer: Assistant Prof. Dr. AYDIN AZIZI

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Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.

Third Edition

Amos Gilat • Vish Subramaniam

Numerical Methods for

Engineers and Scientists

Lecturer: Assistant Prof. Dr. Aydin Azizi

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Lecturer: Assistant Prof. Dr. Aydin Azizi

TAYLOR SERIES EXPANSION OF FUNCTIONS

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Lecturer: Assistant Prof. Dr. Aydin Azizi

APPROXIMATION OF A FUNCTION WITH TAYLOR SERIES EXPANSION

Approximate the function y = sin(x) by using Taylor series expansion about x = 0, using six terms. Using MATLAB, plot the function and the approximation for 0≤x ≤ π.

SOLUTION

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Lecturer: Assistant Prof. Dr. Aydin Azizi

Solving Nonlinear Equations: Newton's method

Algorithm for Newton's method

1. Choose a point xi as an initial guess of the solution.

2. For i=1, 2, . . . , until the error is smaller than a specified value, calculateXi+1 by using following equation:

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Lecturer: Assistant Prof. Dr. Aydin Azizi

Find the solution of the equation 8-4.5(x-sinx) = 0. Use MATLAB with the function NewtonRoot. Use 0.0001 for the maximum relative error and 10 for the maximum number of iterations. use x = 2 as the initial guess of the solution.Solution:

Step 1• Define Newton method function in a new script.

Step 2 • Define f(xi) function in a new script.

Step 3• Define f '(xi) function in a new script.

Step 4• Run defined Newton method function

Solving Nonlinear Equations: Newton's method

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Lecturer: Assistant Prof. Dr. Aydin Azizi

Newton's method : Step #1

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Lecturer: Assistant Prof. Dr. Aydin Azizi

Newton's method : Step #2

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Lecturer: Assistant Prof. Dr. Aydin Azizi

Newton's method : Step #3

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Lecturer: Assistant Prof. Dr. Aydin Azizi

Newton's method : Step #4