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## Stability analysis for some numerical schemes of partial differential equation with extra measurements

#### Nazi ABDOLLAHİ [1] , Davood ROSTAMY [2]

This paper is devoted to study the stability analysis of some finite difference schemes for  an inverse problem with unknowns time-dependent coefficients subject to extra measurements. We prove that the popular forward time centered space scheme is a conditional method. But the backward time centered space and Crank Nicolson methods are suitable schemes because they are unconditional methods. We justify this advantage of the stability analysis versus the some numerical methods with an example. All the results and a numerical example are in two-dimensional setting.
Von Neumann stability analysis, inverse problems, finite difference methods
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Birincil Dil en Matematik Matematik Orcid: 0000-0002-5340-6982Yazar: Nazi ABDOLLAHİ Orcid: 0000-0001-9585-8904Yazar: Davood ROSTAMY (Sorumlu Yazar) Yayımlanma Tarihi : 8 Ekim 2019
 Bibtex @araştırma makalesi { hujms629827, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1324 - 1335}, doi = {10.15672/HJMS.2019.661}, title = {Stability analysis for some numerical schemes of partial differential equation with extra measurements}, key = {cite}, author = {Abdollahi̇, Nazi and Rostamy, Davood} } APA Abdollahi̇, N , Rostamy, D . (2019). Stability analysis for some numerical schemes of partial differential equation with extra measurements . Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1324-1335 . DOI: 10.15672/HJMS.2019.661 MLA Abdollahi̇, N , Rostamy, D . "Stability analysis for some numerical schemes of partial differential equation with extra measurements" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1324-1335 Chicago Abdollahi̇, N , Rostamy, D . "Stability analysis for some numerical schemes of partial differential equation with extra measurements". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1324-1335 RIS TY - JOUR T1 - Stability analysis for some numerical schemes of partial differential equation with extra measurements AU - Nazi Abdollahi̇ , Davood Rostamy Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2019.661 DO - 10.15672/HJMS.2019.661 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1324 EP - 1335 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.661 UR - https://doi.org/10.15672/HJMS.2019.661 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Stability analysis for some numerical schemes of partial differential equation with extra measurements %A Nazi Abdollahi̇ , Davood Rostamy %T Stability analysis for some numerical schemes of partial differential equation with extra measurements %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R doi: 10.15672/HJMS.2019.661 %U 10.15672/HJMS.2019.661 ISNAD Abdollahi̇, Nazi , Rostamy, Davood . "Stability analysis for some numerical schemes of partial differential equation with extra measurements". Hacettepe Journal of Mathematics and Statistics 48 / 5 (Ekim 2019): 1324-1335 . https://doi.org/10.15672/HJMS.2019.661 AMA Abdollahi̇ N , Rostamy D . Stability analysis for some numerical schemes of partial differential equation with extra measurements. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1324-1335. Vancouver Abdollahi̇ N , Rostamy D . Stability analysis for some numerical schemes of partial differential equation with extra measurements. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1324-1335.

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