SEMI-DISCRETIZATION METHOD FOR THE HEAT-EQUATION WITH NONLOCAL BOUNDARY-CONDITIONS

Semi-discretization methods with iterated corrections are considered f or solving the heat equation with boundary conditions containing integ rals over the interior of the interval. The given problem is transform ed into an ordinary differential system of equations, when we substitu te the spatial derivative by finite differences. Such a system is then solved with an implicit integrator together with a quadrature method for the boundary integrals and, for each time step, the numerical sche me - implicit integrator and quadrature method - is repeated iterative ly in order to achieve a given accuracy. The extra work we need with t he iterated corrections enables us to take care of the interrelation o f the solution u (x, t) at the interior and at the boundary points and also to start the numerical process with rough approximations of u (0 , t) and u (1, t).An improvement of the results is achieved when we es timate the local spatial truncation error and make the injection of th at estimation into the ordinary differential system. Numerical experim ents are presented.