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A METHOD FOR SOLVING THE INVERSE PROBLEM OF IDENTIFYING THE SOURCE FUNCTION FOR SYSTEMS WITH DISTRIBUTED PARAMETERS

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This paper considers the inverse problem of identifying the unknown time-dependent source term in a parabolic equation. To solve this problem, a method based on the direct and inverse Laplace transform is proposed. This approach makes it possible to obtain an operator equation describing the explicit dependence of the unknown source function on the boundary function, and then regularization method is used to solve this equation. This eliminates the need to carry out the unstable procedure of numerical inversion in the computational process. The proposed method was used in a computational experiment to obtain a numerical solution of the inverse problem. Results of computational experiment and experimental error estimates of the obtained solutions show sufficient stability and efficiency of the proposed method.

Keywords

inverse source problem; system with distributed parameters; heat conduction; the Laplace transform; regularization method

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UDC

517.9

Pages

1549-1552

References

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Received

2015-05-15

Section of issue

Scientific articles

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