Volume 10, Issue 1
Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel

Marijke Grimmonprez, Karel Van Bockstal & Marián Slodička

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 116-144.

Published online: 2017-10

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  • Abstract

This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.                  

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@Article{NMTMA-10-116, author = {}, title = {Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {1}, pages = {116--144}, abstract = {

This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.                  

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1513}, url = {http://global-sci.org/intro/article_detail/nmtma/12339.html} }
TY - JOUR T1 - Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 116 EP - 144 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1513 UR - https://global-sci.org/intro/article_detail/nmtma/12339.html KW - AB -

This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.                  

Marijke Grimmonprez, Karel Van Bockstal & Marián Slodička. (2020). Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel. Numerical Mathematics: Theory, Methods and Applications. 10 (1). 116-144. doi:10.4208/nmtma.2017.m1513
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