Question: 1. Two-point boundary value problem. with Dirichlet condition. Consider the following second order elliptic boundary value problem in the one-dimensional space: u(;r) = 2, :1:

1. Two-point boundary value problem. with Dirichlet condition. Consider the following second order elliptic boundary value problem in the one-dimensional space: u\"(;r) = 2, :1: 6 ([i1 1), (a) Check that ate} = 55(1 I) is the solution to the above boundary value problem. (b) Discretize the boundary value problem with nite differences on an equidistant grid with h. = 11/4 where the grid points :13:- = to. for i = CI1 - - - ,4 . Write down the associated linear system and determine a numerical approximation to the solution of the boundary value problem by solving this linear system. (c) Compare your numerical solution with the exact one. Explain your observations

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