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(3) Consider the following data generated from a function y = = f(x) 0.15 0.30 0.45 0.60 0.91 0.70 0.40 0.09 x0 y 1.00 Find the best possible finite difference estimate for the derivative f'(0.3). Give a quantitative estimate of the remaining discretisation error. What would be needed to improve your estimate?

(3) Consider the following data generated from a function y = = f(x) 0.15 0.30 0.45 0.60 0.91 0.70 0.40 0.09 x0 y 1.00 Find the best possible finite difference estimate for the derivative f'(0.3). Give a quantitative estimate of the remaining discretisation error. What would be needed to improve your estimate?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(3) Consider the following data generated from a function y = = f(x) 0.60 0.15 0.30 0.45 0.91 0.70 0.40 0.09 x0 y 1.00 Find the best possible finite difference estimate for the derivative f'(0.3). Give a quantitative estimate of the remaining discretisation error. What would be needed to improve your estimate? (4) Consider the equation da(t) dt (20.5 +0.1)e-t, with initial condition z(0) = 1.0. Find an approximate solution to z(1) by evolving the system from t = 0 tot = 1 with a single 2nd-order Runge-Kutta step. Give a rough quantitative estimate of the discretisation error by comparing two different methods or two different step sizes. (5) Write the following second order ODE as a system of 2 first-order ODES: 2 0= d'a q³ dr + dt² m dt (1)
Transcribed Image Text:(3) Consider the following data generated from a function y = = f(x) 0.60 0.15 0.30 0.45 0.91 0.70 0.40 0.09 x0 y 1.00 Find the best possible finite difference estimate for the derivative f'(0.3). Give a quantitative estimate of the remaining discretisation error. What would be needed to improve your estimate? (4) Consider the equation da(t) dt (20.5 +0.1)e-t, with initial condition z(0) = 1.0. Find an approximate solution to z(1) by evolving the system from t = 0 tot = 1 with a single 2nd-order Runge-Kutta step. Give a rough quantitative estimate of the discretisation error by comparing two different methods or two different step sizes. (5) Write the following second order ODE as a system of 2 first-order ODES: 2 0= d'a q³ dr + dt² m dt (1)
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