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As preparation for project one, solve the following boundary value problems in matlab using the two element approximation with nodes at x = 0, x=

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As preparation for project one, solve the following boundary value problems in matlab using the two element approximation with nodes at x = 0, x= /, and x = 1. For each one, plot your numerical solution along with the exact solution. (1 point for Matlab exact solution, 1 for the Galerkin solution, and 1 point for the plot for each one.) a (U,xx-3 = 0 u (0) = 1 (u(1) = 0 b. (u,xx - x = 0 u(0) = 1 (ux (1) = 1 c. (U,xx - 3x = 0 u,x () = 2 ( u(1) = 0 As preparation for project one, solve the following boundary value problems in matlab using the two element approximation with nodes at x = 0, x= /, and x = 1. For each one, plot your numerical solution along with the exact solution. (1 point for Matlab exact solution, 1 for the Galerkin solution, and 1 point for the plot for each one.) a (U,xx-3 = 0 u (0) = 1 (u(1) = 0 b. (u,xx - x = 0 u(0) = 1 (ux (1) = 1 c. (U,xx - 3x = 0 u,x () = 2 ( u(1) = 0

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