Question Description
Using matlab program
Task 1
1. Use the Runge-Kutta method of order 4 to approximate the solution up to 𝑡 = 1 using 5 steps.
2. On a single graph, plot the approximate solution and the exact solution. Compare.
3. Prepare a table showing all “t” values, the approximate solution, exact solution, and absolute
error at all the time steps. Compare.
Task 2
1. Use the approximate solution in Task 1 to construct the natural cubic interpolating splines.
2. On a single graph, plot all cubic splines with 15 points for each, exact solution with 90 points.
Task 3
1. Approximate the integral of the exact solution over the given interval using the composite
Simpson’s rule.
2. Approximate the integral of the exact solution over the given interval using the composite
Simpson’s rule and approximated solution values obtained in Task 1.
3. Approximate the integral of the exact solution over the given interval using the cubic splines
obtained in Task 2.
4. Compare the three results and write your comments.
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