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.

mathematics

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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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