Question

NO CALCULATORS OoR "In applied sciences modeling a system frequently amounts to solving an initial value problem (IVP)." Two ⅣPs are given below. You are asked to solve both problems using MAT LAB's Runge-Kutta 4th-Si. order method discussed in this course. Replace lasiname with your last name in the following steps: 1. Create ONE well-documented driver called Driverlastmame m that employs a menu to solve the problems. Solve the following IVP dy(t) 2. ax +0.5y() - 4e8t, y(0)-2, 0 Sts 20 sec. 3. It is known that the solution to () is y(t) 3.08eat 1.08e 5t (2) Verify that equation (2) is the solution to equation (I) by overlaying the plot of y(0) from (2) on the plot of y(t) from (1). 4. A student is wants to solve the IVP d2y(t) dy(t) 3 o +2y( (t)-4t, 1st S 2 sec. dt2 for which the solution is S/he thinks that ONE of the set of initial conditions shown in (5a) and (5b) (5a) (5b) will give the desired solution for which the relative error- yexactmax Two runs are executed with (5a) used in the first run and (5b) used in the second run. Use condition statermente) and a "Tor loop" to find if (Sa) or (S6) satisfies the relative emor max-yexactmax < S 0.05 the relative error 5. Write the following results to a file, IClastname.dat for ONE of the runs. The output to the file should list the initial conditions, the relative error and whether the initial conditions gives the desired solution. 6. Create a table with the first and last values ONLY for t, y, and yexact, include a table heading.

Answer 1

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