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# hw1305 - ◦ obtain Improved Euler solutions For various...

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Instructors: Dr. I.H. Tuncer Dr. Y. Ozyoruk Assistants: Kenan Cengiz , Gokhan Ahmet AE305 - NUMERICAL METHODS HOMEWORK-I October 19, 2011 Due on: Wednesday, October 26 SECOND ORDER RUNGE-KUTTA METHODS Employ the Improved Euler (Heun’s) method to solve a first order ODE of a physical process, which has an analytical, but non-polynomial solution. In addition, derive a second order RK method (RK2) by choosing p 1 arbitrarily between 0 and 1, and solve the same problem again. You have to modify the Fortran code, euler.f for the numerical solutions. In your report, describe the physical process, the mathematical model and the ODE.
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Unformatted text preview: ◦ obtain Improved Euler solutions For various step sizes, and compare them to the analytical solution and the Euler solution on the same graph. Determine the maximum step size For a convergent solution. ◦ compare the relative error distributions For the various step sizes on the same graph. ◦ compare Improved Euler and RK2 solutions together For the same step sizes, and plot the relative error distributions For various step sizes. ◦ discuss all the results obtained in the previous steps. ◦ include the ±ortran program developed, but no not include any data fles ....
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