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Numerical solution by the quasi-reversibility method of unstable problems for the first-order evolution equation

  • Numerical Methods in Modeling
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Abstract

Prior bounds are derived on the solution of the perturbed problem in different versions of the quasi-reversibility method used for approximate solution of unstable problems for first-order evolution equations. An example of such a problem is provided by the problem backward in time for the equation of heat conduction. Approximate solution of perturbed problems by difference methods is considered. The investigation of the difference schemes of the quasi-reversibility method relies on the general theory of p-stability of difference schemes. Specific features of solution of problems with non-self-adjoint operators are considered. Efficient difference schemes are constructed for multidimensional problems.

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Authors
  1. P. N. Vabishchevich
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Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach. Matematicheskoi Fiziki, pp. 93–124, 1993.

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Vabishchevich, P.N. Numerical solution by the quasi-reversibility method of unstable problems for the first-order evolution equation. Comput Math Model 6, 39–60 (1995). https://doi.org/10.1007/BF01128155

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  • DOI: https://doi.org/10.1007/BF01128155

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