Applied Mathematics 3611F Introduction to Object Oriented Scientific Programming Assignment 3 October 28, 2020 Due: November 18, 2020 Instructor: Dr. Z. Krougly Total of 20 marks [5] 1. Write a program to solve the initial value problem: x 0 = etx with x(2) = 1 on the interval 0 t 2 using Taylor series method. Include terms up to h4. [5] 2. Use input and output files to implement the problem 1. [5] 3. Solve the initial value problem: x 0 = t 2(tx x2) with x(1) = 2 on the interval [1, 3], using four-order Runge-Kutta method and steps h = 1/128. Compare the results with exact (analytical) solutions: x(t) = ( 1 2 + ln t) 1t . Print out the following table for comparison of approximate and exact solutions. k t x Error 0 1.0 2.0 1 ... 10 100 200 256 3.0 [5] 4. For the problems 1, 2, and 3 organize user interface in one C++ project. What to Hand In. Submit the Assignment 3 electronically by OWL (Drop Box): 1) program’s code (questions 1-4) 2) the answers / outputs (questions 1-4), use a separate file (in pdf, word or other doc.) Specify your name, course number, and the assignment number. 1
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