By A. A. Samarskii, Petr N. Vabishchevich

The most sessions of inverse difficulties for equations of mathematical physics and their numerical answer tools are thought of during this ebook that is meant for graduate scholars and specialists in utilized arithmetic, computational arithmetic, and mathematical modelling.

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Here, missing boundary conditions can be identiﬁed, for instance, from measurements performed inside the domain. 46). 47), the following conditions are given: u(0, t) = 0, u(x ∗ , t) = ϕ(t), 0 < t ≤ T. 51) A typical statement of a boundary value inverse problem consists in determining the ﬂux on some part of the boundary inaccessible for measurements (in the case under consideration, at x = l). 51). 48)). We assign to evolutionary inverse problems inverse problems in which initial conditions (lacking in formulation of the problem as a direct problem) need to be identiﬁed.

We present a program that solves the Dirichlet problem for the second-order elliptic equation with variable coefﬁcients and give examples of performed calculations. 1 The difference elliptic problem We consider the matter of approximation for model boundary value problems involving second-order elliptic equations. The present approach is primarily based on using the integro-interpolation method (balance method). It is shown that it is possible to construct an appropriate difference problem on the basis of ﬁnite element approximation.

Write a program and perform computational experiments to examine the rate of convergence of the difference scheme. 3 Boundary value problems for elliptic equations Among stationary mathematical physics problems, problems most important for applications are boundary value problems for second-order elliptic equations. For a model two-dimensional problem, we consider the matter of construction of its discrete analogues with the use of regular rectangular grids on the basis of ﬁnite-difference approximations.