Solution-HW5

# Solution-HW5 - t of the result obtained with Romberg...

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HW#5 Solution 21.8 Integrate the following function using the trapezoidal rule, with n = 1,2,3,4: () + 2 1 2 / 1 dx x x Compute percent relative errors with respect to the true value of 4.8333 to evaluate the accuracy of the trapezoidal approximations. 21.9 Integrate the following function both analytically and using Simpson’s rules, with n = 4 and 5: () + 5 31 3 5 4 dx x Discuss the results.

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22.1 Use Romberg integration to evaluate () + 2 1 2 / 1 dx x x to an accuracy of % 5 . 0 = s ε . Your results should be presented in the form of Fig. 22.3. Use the true value of 4.8333 to determine the true error

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Unformatted text preview: t of the result obtained with Romberg integration. Check that t is less than the stopping criterion s . 22.4 Obtain an estimate of the integral form Prob. 22.1, but using two-, three-, and four-point Gauss-Legendre formulas. Compute t for each case on the basis of the analytical solution. 23.2 Repeat Prob. 23.1, but for y = log x evaluated at x = 20 with h = 2. 23.5 Repeat Prob. 23.4, but for the first derivative of ln x at x = 4 using h 1 = 2 and h 2 =1....
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## This note was uploaded on 01/20/2011 for the course ENG 115 taught by Professor Rocke during the Spring '10 term at UC Davis.

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Solution-HW5 - t of the result obtained with Romberg...

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