Question: (Python Question) 1a.) On solving u xx = f numerically for x (0, 1) with boundary condition u(0) = 0, u(1) = 1. Write a

(Python Question)

1a.) On solving u_xx = f numerically for x (0, 1) with boundary condition u(0) = 0, u(1) = 1.

Write a code to solve it with f(x) = sin(2x) + e^x and the domain (0, 1) subdivided into 100 small intervals.

Write a subroutine to solve the equation with the number of intervals (denoted by m), and the right hand side function f(x) as input.

Pick a right hand side function so that you know the exact solution, run the code, calculate the error, and the convergence order by taking m = 10, 20, 40, 80, 160, 320, 640. Plot the error curve (as a function of the number of intervals) in a way that the convergence order is easily visualized.

1b.) Repeat number 2 with the boundary condition changed to u^'(0) = 0, u(1) = 1 by adopting the first and then the second order treatment of the Neumann boundary condition at 0.

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