Question

Using second order finite differences method with , h = \frac{1}{2}  obtain the system of equations for y_{0^,} y_{1} and y_{2}  for solving the boundary value problem: 

y'' - 5y'+6y = 3

with y(0)-y'(0)=-1 and y(1)+y'(1)=1

21 Mar 2023
Answer :
Word Count : 549

To use the second-order finite differences method with h = 1/2, we first discretize the interval [0, 1] into three grid points:

x_0 = 0, x_1 = 1/2, x_2 = 1

Let y_i be the numerical approximation of y(x_i) for i = 0, 1, 2. We use the second-order finite differences formula to approximate the second derivative of y at each grid point:

y''i ≈ (y{i-1} - 2y_i + y_{i+1})/h^2

Similarly, we use the second-order central differences formula to approximate the first derivative of y at each grid point:

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