title: Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
abstract: This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
authors.affiliation: Via Giovanni Paolo II, 132 - 84084 Fisciano, (Sa), Italy.
authors.forename: Raffaele
authors.initials: R
authors.lastname: D'Ambrosio
authors.affiliation: Via Giovanni Paolo II, 132 - 84084 Fisciano, (Sa), Italy.
authors.forename: Beatrice
authors.initials: B
authors.lastname: Paternoster
keywords: Diffusion problems; Exponentially fitted methods; Finite difference methods; Partial differential equations