ISSN:
1069-8299
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
Semi-discretization methods with iterated corrections are considered for solving the heat equation with boundary conditions containing integrals over the interior of the interval. The given problem is transformed into an ordinary differential system of equations, when we substitute 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 scheme - implicit integrator and quadrature method - is repeated iteratively in order to achieve a given accuracy. The extra work we need with the iterated corrections enables us to take care of the interrelation of 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 estimate the local spatial truncation error and make the injection of that estimation into the ordinary differential system. Numerical experiments are presented.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cnm.1640100910
