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6. Evaluate for the derivative estimate of the function at xi = 0.8 using the step sizes h = 0.01 and h = 0.005 on the following techniques: a. Forward Finite Divided Difference b. Backward Finite Divided Difference c. Centered Finite Divided Difference

6. Evaluate for the derivative estimate of the function at xi = 0.8 using the step sizes h = 0.01 and h = 0.005 on the following techniques: a. Forward Finite Divided Difference b. Backward Finite Divided Difference c. Centered Finite Divided Difference

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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Show your step-by-step solution tabulated solution (similar to the example). Round off computed values to 5 decimal places. Given the function below 1.2 e1.2X cosX -dx 1+0.5x? I = 1. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Trapezoidal rule for n = 8 segments and n = 16 segments. 2. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Simpson's 1/3 rule for n = 16 segments. 3. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Simpson's 3/8 rule for n = 15 segments. 4. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Boole's rule for n = 16 segments. 5. Improve the Trapezoidal rule integral estimate of the function from x = 0 up to x = 1.2 using Romberg Integration for n = 8 segments and n = 16 segments. 6. Evaluate for the derivative estimate of the function at xi = 0.8 using the step sizes h = 0.01 and h = 0.005 on the following techniques: a. Forward Finite Divided Difference b. Backward Finite Divided Difference c. Centered Finite Divided Difference d. Richardson's Extrapolation on all the techniques.
Transcribed Image Text:Show your step-by-step solution tabulated solution (similar to the example). Round off computed values to 5 decimal places. Given the function below 1.2 e1.2X cosX -dx 1+0.5x? I = 1. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Trapezoidal rule for n = 8 segments and n = 16 segments. 2. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Simpson's 1/3 rule for n = 16 segments. 3. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Simpson's 3/8 rule for n = 15 segments. 4. Evaluate for the integral estimate of the function from x = 0 up to x = 1.2 using multiple application Boole's rule for n = 16 segments. 5. Improve the Trapezoidal rule integral estimate of the function from x = 0 up to x = 1.2 using Romberg Integration for n = 8 segments and n = 16 segments. 6. Evaluate for the derivative estimate of the function at xi = 0.8 using the step sizes h = 0.01 and h = 0.005 on the following techniques: a. Forward Finite Divided Difference b. Backward Finite Divided Difference c. Centered Finite Divided Difference d. Richardson's Extrapolation on all the techniques.
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