A Boundary Value Problem with Strong Degeneracy and Local Splines

A new method for solving the singular one-dimensional boundary value problem with a strong degeneracy is proposed in this paper. In the case of the strong degeneration of the differential equation, the boundary condition is set only at one end of the interval. This method is based on the use of the polynomial and non-polynomial Lagrangian and Hermitian type local splines and the variational method. The use of splines of Hermitian type with the first level is convenient if it is needed to obtain simultaneously a solution and the first derivative of the solution at the grid nodes. Next, it is possible to construct the solution between the grid nodes using the same spline approximation formulas. The non-polynomial splines help us to construct a more accurate solution. The results of solving a one-dimensional boundary value problem with strong degeneracy are presented in this paper.