Reprint of Variable-step finite difference schemes for the solution of Sturm–Liouville problems

•We analyze the numerical solution of regular and singular Sturm–Liouville problems.•The developed code uses variable stepsize high order finite difference schemes.•Mesh is adapted according to a strategy of equidistribution of the error.•Solutions are computed according to linear algebra tools.•The software reaches high accuracy and computational efficiency.

We discuss the solution of regular and singular Sturm–Liouville problems by means of High Order Finite Difference Schemes. We describe a method to define a discrete problem and its numerical solution by means of linear algebra techniques. Different test problems are considered to emphasize the behavior of a code based on the proposed algorithm. The methods solve any regular or singular Sturm–Liouville problem, providing high accuracy and computational efficiency thanks to the powerful strategy of stepsize variation.