On Rational Spline Solutions of Differential Equations with Singularities in the Coefficients of the Derivatives

For one generalization of the Riemann differential equation, we obtain sufficient conditions for the approximability by twice continuously differentiable rational interpolation spline functions. To solve the corresponding boundary value problem numerically, a tridiagonal system of linear algebraic equations is constructed and conditions on the coefficients of the differential equation are found guaranteeing the uniqueness of the solution of such a system. Estimates of the deviation of the discrete solution of the boundary value problem from the exact solution on a grid are presented.