2. Apply the Backward-Euler method to the following ordinary differential equation to obtain the approximations at...

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2. Apply the Backward-Euler method to the following ordinary differential equation to obtain the approximations at t= 0.1 and t= 0.2. Compare your results with those of the exact solution u(t)= 1+t du =1+u(t); u(0) = 1 dt 1+ d'u 3. Show that the fourth centered divided difference approaching to dx Where x is a point belonging to a uniform mesh of size h, it is given by Uk-2 − AUx-1 +6Uk − AUx+1 +Ux+2 +0(h²) hª 2. Apply the Backward-Euler method to the following ordinary differential equation to obtain the approximations at t= 0.1 and t= 0.2. Compare your results with those of the exact solution u(t)= 1+t du =1+u(t); u(0) = 1 dt 1+ d'u 3. Show that the fourth centered divided difference approaching to dx Where x is a point belonging to a uniform mesh of size h, it is given by Uk-2 − AUx-1 +6Uk − AUx+1 +Ux+2 +0(h²) hª