The analysis of initial-boundary-value problems using Hermite interpolation

Hermite methods for hyperbolic initial-boundary value problems

We study arbitrary-order Hermite difference methods for the numerical solution of initial-boundary value problems for symmetric hyperbolic systems. These differ from standard difference methods in that derivative data (or equivalently local polynomial expansions) are carried at each grid point. Time-stepping is achieved using staggered grids and Taylor series. We prove that methods using deriva...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Complementary Lidstone Interpolation and Boundary Value Problems

1 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA 2 Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3 Department of Mathematics, Azores University, R. Mãe de Deus, 9500-321 Ponta Delgada, Portugal 4 School of ELectrical & Electronic Engineering, Nanyang Technological University, Sin...

Barycentric Hermite Interpolants for Event Location in Initial-Value Problems

Continuous extensions are now routinely provided by many IVP solvers, for graphical output, error control, or event location. Recent developments suggest that a uniform, stable and convenient interpolant may be provided directly by value and derivative data (Hermite data), because a new companion matrix for such data allows stable, robust and convenient root-finding by means of (usually built-i...

Solutions of initial and boundary value problems via F-contraction mappings in metric-like space

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...