In this paper, we study a two-point boundary value problem consisting of the heat equation on open interval (0,1) with conditions which relate first and second spatial derivatives at points. Moreover, unique solution to can be represented probabilistically in terms sticky Brownian motion. This probabilistic representation is attained from stochastic differential for motion bounded [0,1].

Aims: In this paper an approximate method for the solution of third-order differential equation with two and three point boundary condition is developed using iterative reproducing kernel method. Methods: The third order boundary value problem is converted into integro-differential equation of second order two point boundary value problem. The reproducing kernel method which takes the form of a...

A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Caputo fractional derivative of order δ with 1 < δ < 2. Writing u for the solution of the problem, it is known that typically u′′(x) blows up as x→ 0. A numerical example demonstrates the possibility of a further phenomenon that imposes difficulties on numerical meth...