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 frst 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 ±ortran 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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This note was uploaded on 10/24/2011 for the course AEE 305 taught by Professor Ss during the Spring '11 term at Middle East Technical University.

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