Consider the boundary value problem -u +2u'- u= 1 u=1 u= -1 for 0 < x...

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Consider the boundary value problem -u" +2u'- u= 1 u=1 u= -1 for 0 < x < 2, at x = 0, at x = 2. (i) Set up a finite difference approximation as explained in lectures with P (ii) Eliminate the variables U_0 and US to obtain a 4by-linear system. (iii) Solve the linear system for U_1,U_2...... (iv) Compare graphically between exact and approximate solutions (v) Compute the maximum errors for h=1/4, 1/8,1/16,1/32 and 1/64. Then, compute the convergence rates. Consider the boundary value problem -u" +2u'- u= 1 u=1 u= -1 for 0 < x < 2, at x = 0, at x = 2. (i) Set up a finite difference approximation as explained in lectures with P (ii) Eliminate the variables U_0 and US to obtain a 4by-linear system. (iii) Solve the linear system for U_1,U_2...... (iv) Compare graphically between exact and approximate solutions (v) Compute the maximum errors for h=1/4, 1/8,1/16,1/32 and 1/64. Then, compute the convergence rates.

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To solve the boundary value problem using finite difference approximation we can follow these steps i Set up a finite difference approximation We can ... View the full answer