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Coefficient inverse problems related to identifying the right-hand side of anequation with use of additional information is of interest among inverseproblems for partial differential equations. When considering non-stationaryproblems, tasks of recovering the dependence of the right-hand side on time andspatial variables can be treated as independent. These tasks relate to a classof linear inverse problems, which sufficiently simplifies their study. Thiswork is devoted to a finding the dependence of right-hand side ofmultidimensional parabolic equation on spatial variables using additionalobservations of the solution at the final point of time - the finaloverdetermination. More general problems are associated with some integralobservation of the solution on time - the integral overdetermination. The firstmethod of numerical solution of inverse problems is based on iterative solutionof boundary value problem for time derivative with non-local acceleration. Thesecond method is based on the known approach with iterative refinement ofdesired dependence of the right-hand side on spacial variables. Capabilities ofproposed methods are illustrated by numerical examples for modeltwo-dimensional problem of identifying the right-hand side of a parabolicequation. The standard finite-element approximation on space is used, the timediscretization is based on fully implicit two-level schemes.

Iterative computational identification of a spacewise dependent the source in a parabolic equations