Abstract
- We study difference schemes with indefinite coefficients and indefinite right-hand sides on stencils that consist of any number of arbitrarily located points. In the two-dimensional case we obtain linear systems of equations for the calculation of coefficients in ordinary (noncompact) and compact schemes and conditions on the right-hand side under which the approximation order of differential equations would be equal to a predetrmined natural number. Analogously we study the behaviour of ordinary and compact approximations of universal boundary conditions, including the conditions of the first, second, and third kinds. In the three-dimensional case we establish the number of conditions which specify coefficients and the right-hand sides of schemes. We consider particular examples of schemes in the plane and in the space.
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