Problem 4. For the 2-point BVP: -u (x) + 4u - sin(u)=0 on 0 x 1...

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Problem 4. For the 2-point BVP: -u" (x) + 4u - sin(u)=0 on 0 x 1 with u(0)=u(1)=0. i) (1 point) Write down the main procedures of the shooting method for the BVP with the unknown parameter u'(0)=a, ii) (2 points) Propose a numerical method for the solution of the IVP u" (x) = -2u+sin(u) on 0 < x < 1 with u(0)=0 and u'(0)=a, and a method for solving the resulting nonlinear equation for a. State a simple reason to support your proposed choices. Problem 4. For the 2-point BVP: -u" (x) + 4u - sin(u)=0 on 0 x 1 with u(0)=u(1)=0. i) (1 point) Write down the main procedures of the shooting method for the BVP with the unknown parameter u'(0)=a, ii) (2 points) Propose a numerical method for the solution of the IVP u" (x) = -2u+sin(u) on 0 < x < 1 with u(0)=0 and u'(0)=a, and a method for solving the resulting nonlinear equation for a. State a simple reason to support your proposed choices.