Numerical Techniques for Engineering Problems

1. Write a general-purpose computer program to solve the second-order ODE given on [1, 3] by using
Adams-Moulton and Runge-Kutta-Fehlberg methods. Examine the effect of step size on the results. (15
p)

2. Write a general-purpose computer program to find the minimum value of a function by using golden ratio
bisection and parabolic second-order extrapolation technique. Find the minimum of the function ?(?) =
?
?/2 + ???2
(?) − ???5
(?) within the interval [-3, 2]. (15 p)

3. Solve the heat transfer-equation on [a, b] by using finite-differences method. (10 p) Write a computer program to solve the above BVP. Examine the effect of ∆?, ? on the results. Consider
3 different values for these parameters and present your results graphically.

4. Write a computer program to find the eigenvalues of the following matrix by using QR method. (10 p)

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