HW_Assignment_6 - HOMEWORK ASSIGNMENT 6 EGM 3344 Numerical...

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Unformatted text preview: HOMEWORK ASSIGNMENT 6 EGM 3344 Numerical Integration of Functions Concepts Problems from Chapra book chapters 17 through 19 Approach Comments Matlab Do all parts. Part (f) is single application Simpson’s 3/8 rule. Matlab For part (c), use the combination of the trapezoidal and Simpson’s rules that will produce the most accurate solution. Matlab Matlab Review section 18.2 in the book for how to calculate a for Romberg integration. Note that s is the desired value of a . Report t for each part given that the analytical solution for the integral is 41.17107385. Matlab Use the finite difference equations in Figs. 19.3 through 19.5. Matlab Only use one application of Richardson’s extrapolation. Matlab Your Matlab program should do the following: 1) Take x and y values as inputs. 2) Spline fit the data points using the built-in Matlab function spline to find the piecewise polynomial coefficients. 3) Calculate the piecewise polynominal coefficients for the first derivative of the spline function 4) Use the first derivative piecewise polynominal coefficients to calculate the first derivative of the spline curve at the original x values using the built-in Matlab function ppval. Matlab Use the built-in Matlab function gradient with a step size of 25. Problem 17.2 17.5 17.6 18.3 19.1 19.4 19.9 19.11 Answers 17.2 (a) 3.500167731 (b) 1.99320, t = 42.88% (c) n = 2, 2.96303, t = 15.35% n = 4, 3.3437, t = 4.47% (d) 3.28427, t = 6.17% (e) 3.47059, t = 0.84% (f) 3.388365, t = 3.19% 17.5 (a) 0.79124 (b) 0.79284, (c) 0.791282, t = 0.2022% t = 0.0052% 2 17.6 (a) 2.666667 (b) 2, t = 25% (c) 2.666667, t = 0% 18.3 (a) 41.21305531, a = 0.3579%, t = 0.1020% (b) 39.6075058, t = 3.8% (c) quad solution 41.17107385090233, t = 1.1e-8% quadl solution 41.17107466800178, t = 2e-6% 19.1 19.4 D = -0.70539 19.9 True derivative values = -0.3012 -0.4979 -0.4484 -0.1348 -0.0274 Spline fit derivative values = -0.5873 -0.4952 -0.4496 -0.1286 -0.0581 1.1600 0.9200 0.6800 0.4400 0.3200 -0.0096 -0.0096 -0.0072 -0.0048 19.11 Velocity = 1.2800 Acceleration = -0.0048 -0.0072 ...
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