FEM1D_SPECTRAL_NUMERIC is a MATLAB program which applies the spectral finite element method to solve the problem u = - pi^2 sin(x) over [-1,+1] with zero boundary conditions, using as basis elements the functions x^n*(x-1)*(x+1), and carrying out the integration numerically using MATLAB s quad() function. This function solves the problem u = - pi^2 * sin( pi * x ) for x in (-1,1), with boundary conditions u(-1) = u(1) = 0.-FEM1D_SPECTRAL_NUMERIC is a MATLAB program which applies the spectral finite element method to solve the problem u　 = - pi^2 sin(x) over [-1,+1] with zero boundary conditions, using as basis elements the functions x^n*(x-1)*(x+1), and carrying out the integration numerically using MATLAB s quad() function. This function solves the problem u　 = - pi^2 * sin( pi * x ) for x in (-1,1), with boundary conditions u(-1) = u(1) = 0.