LABS 4_5

1. 
Design an iterative method for the solution of BVP y''=6*t, y(0)=0 and y(1)=1, using forth order Runge-Kutta method in the shooting method. Use time step h=0.5. Test your method for the initial slopes y'(0)=1, y'(0)=-1, and y'(0)=0. Plot your results and identify the correct solution. (See example from notes.).
2.
Solve the exercise 1. again, using Matlab function ode45 instead of RK. Plot your results.
3.
Study the function "bvp_nonlinear" and explain how it works.
4.
Study the function "bvp_matlab2" and explain how it works. Change the differential equation in such a way that it will describe the damped oscillations. Is there a situation when the oscillations disappear? If yes, describe this situation.
5.
Solve BVP y''=-4, y(0)=0 and y(1)=1, using finite differences and time step h=0.5.
6.
Solve BVP y''= y, y(0)=0 and y(1)=1, using collocation method and time step h=0.5.
7.
Solve BVP y''=-6*t, y(0)=0 and y(1)=1, using linear B-splines and Galerkin method with time step h=0.5.

Pack your solutions in a zip file, set permissions for reading, and save your file in the directory:
/home/scicomp/trobec/labs due to Thursday.