# 5DV005 Lab5 Solved

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Problem 1 Consider the problem of computing the derivative f0(x) using the finite difference approximation

Execute the script rdifmwe1 and examine output in detail:

1. Determine the value of k where the computed value of Richardsonâ€™s fraction has executed an illegal jump.
2. Determine the range of k values for which the computed value of Richardsonâ€™s fraction convergences monotonically to 2p for a suitable value of p.
3. Determine the range of k values for which the computed value of Richardsonâ€™s fraction converges to 2p at the correct rate.
4. Determine the range of k values where the error estimates become more and more accurate.
5. How is the behavior of Richardsonâ€™s fraction related to the quality of Richardsonâ€™s error estimate?

Problem 2 Copy rdifmwe1.m into /work/l5p2.m and adapt it to the problem of computing f0(2) where f(x) = ex sin(x)

Do not include the derivative when you call rdif.

1. Verify that the computed value of Richardsonâ€™s fraction appears to converge towards 2p for a suitable value of p as h tends to zero.
2. Find the last value of k, where the computed value of Richardsonâ€™s fraction behaved exactly as predicted for the exact value of Richardsonâ€™s fraction.
3. Include the exact derivative when you call rdif. Find the value of k where the accuracy of Richardsonâ€™s error estimate is maximal.
4. How is the behavior of Richardsonâ€™s fraction related to the quality of Richardsonâ€™s error estimate?

Problem 3 Consider the problem of computing the derivative f0(x) using the finite difference approximation

Execute the script rdifmwe2 and examine output in detail:

1. Determine the value of k where the computed value of Richardsonâ€™s fraction has executed an illegal jump.
2. Determine the range of k values for which the computed value of Richardsonâ€™s fraction convergences monotonically to 2p for a suitable value of p.
3. Determine the range of k values for which the computed value of RichRichardsonâ€™s fraction converges to 2p at the correct rate.
4. Determine the range of k values where the error estimates become more and more accurate.
5. Is the behavior of Richardsonâ€™s fraction related to the quality of Richardsonâ€™s error estimate?

Problem 4 Copy rdifmwe2.m into /work/l5p4.m and adapt it to the problem of computing f0(2) where f(x) = ex sin(x).

Do not include the derivative when you call rdif initially.

1. Verify that the computed value of Richardsonâ€™s fraction appears to converge towards 2p for a suitable value of p as h tends to zero.
2. Find the last value of k, where the computed value of Richardsonâ€™s fraction behaved exactly as predicted for the exact value of Richardsonâ€™s fraction.
3. Include the exact derivative when you call rdif. Find the value of k where the accuracy of Richardsonâ€™s error estimate is maximal.
4. Is the behavior of Richardsonâ€™s fraction related to the quality of Richardsonâ€™s error estimate?
• lab5-6efell.zip