practical04 - COSC 1002/1902 Computational Science in C...

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Practical 4 This practical session involves writing codes to numerically integrate using the trapezoidal rule, and also includes the use of arrays in C, the procedure for reading data from file using redirection, and additional practice in the use of gnuplot. Before you begin these exercises, you should review the material in lecture 4. You should also download the codes appearing in the lecture notes for lecture 4, arrays.c , scan fact.c , and passing.c , which are available via WebCT or from the website http://www.physics.usyd.edu.au/ wheat/cosc1002 . Compile and run each of the codes, following the steps outlined in the lecture notes, and confirm that you obtain the results described in the lecture notes. Also try producing the file sinc.txt with arrays.c and then plotting it using gnuplot, as described in the lecture. If you succeed with this then you are ready to begin the exercises. If not consult a tutor, who can provide assistance. The exercises are for students in both units except where indicated (‘1002’ means that the question is just for students in COSC 1002, and ‘1902’ means that the question is just for students in COSC 1902). Remember to have a tutor mark off checkpoints as you reach them. Exercises 1. As explained in lecture 4, the trapezoidal rule gives an approximate value for the integral of a function f ( x ) between x = a and x = b in terms of evaluations f i = f ( x i ) of the function at points x i ( i = 0 , 1 , 2 , ..., N - 1 ) such that x 0 = a , x N - 1 = b , and x 0 < x 1 < x 2 < ... < x N - 1 . Specifically, the extended trapezoidal rule is Z b a f ( x ) dx N - 2 X i =0 1 2 Δ x i ( f i + f i +1 ) , (1) where Δ x i = x i +1 - x i . The goal of this exercise is to write a code to estimate I = Z 1 0 ± x + 1 2 ² dx (2) using the extended trapezoidal rule, i.e. equation (1). (a) Evaluate the integral in equation (2) analytically (i.e. using only pen and paper.)
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practical04 - COSC 1002/1902 Computational Science in C...

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