Numerical solution and distinguishability in time fractional parabolic equation
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Date
2015
Authors
Demir, Ali
Kanca, Fatma
Ozbilge, Ebru
Journal Title
Journal ISSN
Volume Title
Publisher
Springer International Publishing Ag
Abstract
This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output mappings in the linear time fractional inhomogeneous parabolic equation D(t)(alpha)u(x t) = (k(x)u(x))(x) + r(t)F(x t) 0 < alpha = 1 with mixed boundary conditions u(0 t) = psi(0)(t) u(x)(1 t) = psi(1)(t). By defining the input-output mappings Phi[center dot] : kappa -> C-1[0 T] and psi[center dot] : kappa -> C[0 T] the inverse problem is reduced to the problem of their invertibility. Hence the main purpose of this study is to investigate the distinguishability of the input-output mappings Phi[center dot] and psi[center dot]. Moreover the measured output data f (t) and h(t) can be determined analytically by a series representation which implies that the input-output mappings Phi[center dot] : kappa -> C-1[0 T] and psi[center dot] : kappa -> C[0 T] can be described explicitly where Phi[r] = k(x)u(x)(x t
r)vertical bar(x= 0) and psi[r] = u(x t
r)vertical bar(x= 1). Also numerical tests using finite difference scheme combined with an iterative method are presented.
r)vertical bar(x= 0) and psi[r] = u(x t
r)vertical bar(x= 1). Also numerical tests using finite difference scheme combined with an iterative method are presented.
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Citation
10
WoS Q
N/A
Scopus Q
Q3