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.