Applications to ODEs, PDEs and EVPs of high order Finite Differece schemes

The aim of this talk is an overview on several numerical applications of a family of high order finite difference schemes named HOGUP. These numerical methods, based on the same numerical schemes, allows to develop different approaches, which are suitable to figure out different kinds of problems. Firstly, it considers the solution of second order boundary and initial value problems, in particular of the singular perturbation problems [1] and stiff initial value problems [2]. Then, it shows the application of these numerical schemes to some multiparameter spectral problems, as the Sturm-Liouville problems [3, 4, 5]. Finally, it considers the solution of partial differential equations, focusing on reaction-diffusion problems[6].