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

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
Software:
COLROW
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