Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Write a MATLAB Script-M file to solve each of the following problems.
| No. | Problem |
| 1. | Use the Bisection method to find an approximation with accuracy 10β5,Β to a value in [0.5, [1].5] for π(π₯) = ex β 2 β cos(β‘ex β 2). Show your answer in a table with headings as follows: βIteration No.β, βaβ, βbβ, βπβ,
β|β‘π(π)|β |
| 2. | Express the following equation as a fixed-point problem π₯β‘ = β‘π(π₯) in three different ways
x3 β‘β β‘xβ‘ +β‘ex β‘= β‘0 Use Fixed Point Iteration Method to find an approximation with accuracy 10β5. Show your answers in a table with suitable headings. Comment on the convergence of choices of π(π₯). |
| 3. | Set πβ‘(π₯) β‘= β‘54π₯6 β‘+ β‘45π₯5 β‘β β‘102π₯4 β‘β β‘69π₯3 β‘+ β‘35π₯2 β‘+ β‘16π₯β‘ β β‘4. Plot the function on the interval [β2, 2], and use the Secant Method to find all five roots in the interval. Show your results in a table with headings as follows:
βIteration No.β, βπ₯πβ, βπ΄ππ β‘πππππβ. |
| 4. | Apply Newtonβs Method to find both roots of the function
πβ‘(π₯)β‘= β‘14π₯ππ₯β2 β‘β β‘12ππ₯β2 β‘β 7π₯3 β‘+ β‘20π₯2 β‘β β‘26π₯β‘ + β‘12Β on the interval [0, 3]. Print out the sequence of iterations, the errors ππ, and the relevant error ratio . |
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