Chebyshev collocation method for solving second order ODEs using integration matrices

The spectral collocation method for solving two-point boundary value problems second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. approach allows a stable calculation of both representation and its pointwise any required grid definition domain equation additional conditions multipoint problem. For effective construction SLAE, which gives desired coefficients, matrices integration are actively used. proposed algorithms have high accuracy moderate-dimension systems linear algebraic equations. matrix system remains well-conditioned and, with increase number points, finding solutions ever-increasing accuracy.