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Question: 5 the boundary value problem cud2 u3x 0 gve uoand...

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5 The boundary value problem C(u)d2 u3x 0 gve u(o)and u(1) 1 is to be solved by the weighted residual method (i) Determine which of the two trial functions, U(x) or l½(x), automatically satisfies the boundary conditions: UM(x)-x)+ax(1-x) ox(1-x2) (x) x + c1(x2-x) + c2(x3-x) = (i) Determine the residual C(U)(x) associated with your chosen trial function and then, by applying the weight functions w(x) 1 and w(x) x in turn, use the condition 10 w/(x) R(x) dx = 0 to derive two algebraic equations for c and c. Solve these equations working correct to four decimal places. (ili) Given that the exact solution is given by u(x)Be 3 where A-0.06656, B0.06656, then perform a check on your approximate solution, U(x), by computing the difference u(0.5) U(0.5)

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