Relationship between Interpolation and Differential Equations: A Class of Collocation Methods [chapter]

Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli
2017 Dynamical Systems - Analytical and Computational Techniques  
In this chapter, the connection between general linear interpolation and initial, boundary and multipoint value problems is explained. First, a result of a theoretical nature is given, which highlights the relationship between the interpolation problem and the Fredholm integral equation for high-order differential problems. After observing that the given problem is equivalent to a Fredholm integral equation, this relation is used in order to determine a general procedure for the numerical
more » ... the numerical solution of high-order differential problems by means of appropriate collocation methods based on the integration of the Fredholm integral equation. The classical analysis of the class of the obtained methods is carried out. Some particular cases are illustrated. Numerical examples are given in order to illustrate the efficiency of the method.
doi:10.5772/66995 fatcat:dmxkhcuh4bfjbgr3v7fweuikzy