Year 2019, Volume 48 , Issue 5, Pages 1324 - 1335 2019-10-08

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

Nazi Abdollahi [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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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-5340-6982
Author: Nazi Abdollahi

Orcid: 0000-0001-9585-8904
Author: Davood Rostamy (Primary Author)

Dates

Publication Date : October 8, 2019

Bibtex @research article { hujms629827, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1324 - 1335}, doi = {}, title = {Stability analysis for some numerical schemes of partial differential equation with extra measurements}, key = {cite}, author = {Abdollahi, Nazi and Rostamy, Davood} }
APA Abdollahi, 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 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/49321/629827
MLA Abdollahi, 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 <https://dergipark.org.tr/en/pub/hujms/issue/49321/629827>
Chicago Abdollahi, 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 Abdollahi , Davood Rostamy Y1 - 2019 PY - 2019 N1 - DO - 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 - UR - 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 Abdollahi , 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 %U
ISNAD Abdollahi, Nazi , Rostamy, Davood . "Stability analysis for some numerical schemes of partial differential equation with extra measurements". Hacettepe Journal of Mathematics and Statistics 48 / 5 (October 2019): 1324-1335 .
AMA Abdollahi 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 Abdollahi 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): 1335-1324.