The mathematical problem is a second-order differential equation with set boundary conditions. It can be solved using a numerical method known as the central difference approximation. This approach divides the range into equidistant points, creating a system of linear equations that yields the values of u(x).
The given equation is a second-order differential equation coupled with two boundary conditions. This can be solved using the central difference approximation – a common method used in numerical analysis. You divide the interval [0,1] into equidistant points, producing a linear system of equations that can be solved for the values of u(x).
With the boundary conditions u(0)=0, and u'(1)=10, and the second central difference approximation, the equation -u''(x)=f(x) turns into a linear system: -u[i+1] + 2u[i] - u[i-1] = h2f[i], for i from 1 to n-1, where h is the space between points. For the boundary values, we have u[0]=0 and -u[n-1]+u[n]=h*10.
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