TY - JOUR

T1 - Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

AU - Aldoghaither, Abeer

AU - Liu, Da-Yan

AU - Laleg-Kirati, Taous-Meriem

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/12/2

Y1 - 2015/12/2

N2 - In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

AB - In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

UR - http://hdl.handle.net/10754/592619

UR - http://epubs.siam.org/doi/10.1137/15M1008993

UR - http://www.scopus.com/inward/record.url?scp=84953284912&partnerID=8YFLogxK

U2 - 10.1137/15M1008993

DO - 10.1137/15M1008993

M3 - Article

VL - 37

SP - A2813-A2839

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 6

ER -