The reformulation and numerical solution of certain nonclassical initial- boundary value problems. (English) Zbl 0722.65062

Fairweather, Graeme; Saylor, Rick D.

SIAM J. Sci. Stat. Comput. 12, No. 1, 127-144 (1991).

The paper presents examples of problems with non-local boundary conditions and indications how each problem can be converted to one with separated boundary conditions. The price one pays for this modification is an increase of one in the number of partial differential equations for each nonlocal condition. However, the additional equations are straightforward and the augmented problem can easily be handled using standard numerical techniques (POST or SPRINT software packages for example).

Reviewer: Ju.V.Kostarchuk (Chernigov)

MSC:

65Z05	Applications to the sciences
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65R20	Numerical methods for integral equations
35K15	Initial value problems for second-order parabolic equations
35L15	Initial value problems for second-order hyperbolic equations
45K05	Integro-partial differential equations

Keywords:

nonclassical parabolic and hyperbolic initial-boundary value problems; chemical diffusion; heat conduction; thermoelasticity; population dynamics; nuclear reactor dynamics; finite-difference method; numerical experiments; Crank-Nicolson finite-element Galerkin method; partial integrodifferential equations; Keller’s box scheme; non-local boundary conditions

Software:

COLROW