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

Authors : Nazi ABDOLLAHİ, Davood ROSTAMY

Pages : 1324-1335

Doi:10.15672/HJMS.2019.661

View : 19 | Download : 4

Publication Date : 2019-10-08

Article Type : Research Paper

Abstract :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.
Keywords : Von Neumann stability analysis, inverse problems, finite difference methods