TY - JOUR
T1 - Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks
AU - Avazzadeh, Zakieh
AU - Nikan, Omid
AU - Tenreiro Machado, José
AU - Rasoulizadeh, Mohammad Navaz
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/12
Y1 - 2022/12
N2 - This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.
AB - This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.
KW - Caputo fractional derivative
KW - Finite difference
KW - Local meshless method
KW - RBF
KW - Stability
KW - Time-fractional Sobolev equation
UR - http://www.scopus.com/inward/record.url?scp=85133010993&partnerID=8YFLogxK
U2 - 10.1186/s13662-022-03720-w
DO - 10.1186/s13662-022-03720-w
M3 - Article
AN - SCOPUS:85133010993
SN - 2731-4235
VL - 2022
JO - Advances in Continuous and Discrete Models
JF - Advances in Continuous and Discrete Models
IS - 1
M1 - 48
ER -