9) For a second order ordinary differential equation: y + y = 0 find the analytical...

 

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9) For a second order ordinary differential equation: y" + y = 0 find the analytical solution y(x) for the boundary value problem: (y(0) = 0 (y(1) = 3 Then create sets of algebraic equations using second order differential schemes for the first and second derivative for nodes N = 6 and N = 11 on the interval [0, 1] and solve them numerically using Matlab/Octave. Compare local errors in individual nodes (i.e. the difference between the numerical and analytical solution). On their basis, estimate the order of the method. 9) For a second order ordinary differential equation: y" + y = 0 find the analytical solution y(x) for the boundary value problem: (y(0) = 0 (y(1) = 3 Then create sets of algebraic equations using second order differential schemes for the first and second derivative for nodes N = 6 and N = 11 on the interval [0, 1] and solve them numerically using Matlab/Octave. Compare local errors in individual nodes (i.e. the difference between the numerical and analytical solution). On their basis, estimate the order of the method.