Gegenbauer Cardinal Functions for the Inverse Source Parabolic Problem with a Time-Fractional Diffusion Equation

Rostamy, Davood; Abdollahi, N.

doi:10.1080/23324309.2017.1352514

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“…In the past several decades, various numerical techniques have been developed to solve inverse problems [3,10,14,15,21]. In these problems extra measurement data are used to obtain unique solution.…”

Section: Introductionmentioning

confidence: 99%

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

Nazi¹,

Rostamy²

2019

HJMS

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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.Mathematics Subject Classification (2010). 65M12, 65M15, 65M60, 82D10, 35L80

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