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Given the function y(x) = sin(4+ sin(2x)) and the mesh x₁ = xo + ik, where co ㅠ 2' ㅠ determine the central finite difference for the first derivative of y with step size k = 14 (c) Enter the absolute error at mesh point i = 4. At the same point, also calculate the exact first derivative y'(x). Calculate the absolute value of the error of the finite difference approximation at the point x₁. Work to at least 6 decimal places throughout and enter your answers to 2 decimal places. (a) Enter the finite difference approximation (b) Enter the exact derivative

Given the function y(x) = sin(4+ sin(2x)) and the mesh x₁ = xo + ik, where co ㅠ 2' ㅠ determine the central finite difference for the first derivative of y with step size k = 14 (c) Enter the absolute error at mesh point i = 4. At the same point, also calculate the exact first derivative y'(x). Calculate the absolute value of the error of the finite difference approximation at the point x₁. Work to at least 6 decimal places throughout and enter your answers to 2 decimal places. (a) Enter the finite difference approximation (b) Enter the exact derivative

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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Given the function y(x): = sin(4 + sin(2x)) and the mesh x₁ = xo + ik, where co determine the central finite difference for the first derivative of y with step size k - ㅠ 2 (c) Enter the absolute error ㅠ 14 At the same point, also calculate the exact first derivative y'(xi). Calculate the absolute value of the error of the finite difference approximation at the point ï¿. Work to at least 6 decimal places throughout and enter your answers to 2 decimal places. (a) Enter the finite difference approximation (b) Enter the exact derivative Select at mesh point į = 4. (d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of
Transcribed Image Text:Given the function y(x): = sin(4 + sin(2x)) and the mesh x₁ = xo + ik, where co determine the central finite difference for the first derivative of y with step size k - ㅠ 2 (c) Enter the absolute error ㅠ 14 At the same point, also calculate the exact first derivative y'(xi). Calculate the absolute value of the error of the finite difference approximation at the point ï¿. Work to at least 6 decimal places throughout and enter your answers to 2 decimal places. (a) Enter the finite difference approximation (b) Enter the exact derivative Select at mesh point į = 4. (d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of
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