Consider the 2-point BVP: -u + u' + 2u=1x for 0 < x ...

 

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Consider the 2-point BVP: -u" + u' + 2u=1x for 0 < x <1 with u(0)=u(1)=0. i) (2 points) On a uniform grid {r=ih=1} in [0,1], find a finite difference approximation to the BVP with a truncation error of order O(h2). Specify the difference approximations (numerical differentiation rules) used for each derivative term, and show the resulting linear algebraic system (the coefficient matrix and the right-hand side vector). Consider the 2-point BVP: -u" + u' + 2u=1x for 0 < x <1 with u(0)=u(1)=0. i) (2 points) On a uniform grid {r=ih=1} in [0,1], find a finite difference approximation to the BVP with a truncation error of order O(h2). Specify the difference approximations (numerical differentiation rules) used for each derivative term, and show the resulting linear algebraic system (the coefficient matrix and the right-hand side vector).