Open AccessAn efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions
Author(s) -
Fouad Mohammad Salama,
Nur Nadiah Abd Hamid,
Norhashidah Hj. Mohd. Ali,
Umair Ali
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022134
Subject(s) - mathematics , discretization , laplace transform , convergence (economics) , fractional calculus , stability (learning theory) , group (periodic table) , diffusion equation , space (punctuation) , transformation (genetics) , iterative method , mathematical analysis , algorithm , computer science , biochemistry , chemistry , economy , organic chemistry , service (business) , machine learning , economics , gene , economic growth , operating system
In this paper, a new modified hybrid explicit group (MHEG) iterative method is presented for the efficient and accurate numerical solution of a time-fractional diffusion equation in two space dimensions. The time fractional derivative is defined in the Caputo sense. In the proposed method, a Laplace transformation is used in the temporal domain, and, for the spatial discretization, a new finite difference scheme based on grouping strategy is considered. The unique solvability, unconditional stability and convergence are thoroughly proved by the matrix analysis method. Comparison of numerical results with analytical and other approximate solutions indicates the viability and efficiency of the proposed algorithm.