Fractional boundary value problems: Analysis and numerical methods

High Order Numerical Methods for Fractional Terminal Value Problems

In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. We provide a convergence analysis of the numerical method, derived based upon properties of the equation being solved and without the need to impose smoothness conditions on the solution. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method...

Numerical Methods for Two–Point Boundary Value Problems

Various Numerical Methods for Singularly Perturbed Boundary Value Problems

As Science & technology develop, many practical problems, such as the mathematical boundary layer theory or approximation of solution of various problems described by differential equations involving large or small parameters have become increasingly complex and therefore require the use of asymptotic methods. However, the theory of asymptotic analysis for differential operators has mainly been...

On Numerical Methods for Elliptic Transmission/boundary Value Problems

The use of numerical tools to solve challenging problems in mathematics has exploded in the past several decades. The purpose of this paper is to compare the results of two different types of numerical methods in finding solutions to the eigenvalue problem for a second-order elliptic differential equation subject to boundary and transmission conditions. The transmission conditions result from j...

Shooting Methods for Numerical Solution of Stochastic Boundary-Value Problems

In the present investigation, numerical methods are developed for approximate solution of stochastic boundary-value problems. In particular, shooting methods are examined for numerically solving systems of Stratonovich boundary-value problems. It is proved that these methods accurately approximate the solutions of stochastic boundary-value problems. An error analysis of these methods is perform...