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Numerical solution of the multiterm time‐fractional diffusion equation based on reproducing kernel theory
Author(s) -
Hemati Farshad,
Ghasemi Mehdi,
Khoshsiar Ghaziani Reza
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22518
Subject(s) - kernel (algebra) , mathematics , convergence (economics) , hilbert space , reproducing kernel hilbert space , diffusion equation , diffusion , series (stratigraphy) , mathematical analysis , basis (linear algebra) , space (punctuation) , geometry , computer science , pure mathematics , paleontology , physics , operating system , economy , service (business) , biology , economics , thermodynamics , economic growth
In this study, we present an efficient computational method for finding approximate solution of the multi term time‐fractional diffusion equation. The approximate solution is presented in the form of a finite series in a reproducing kernel Hilbert space. The convergence of proposed method is studied under some hypothesis which provides the theoretical basis of proposed method for solving the considered equation. Finally, some numerical experiments are considered to examine the efficiency of proposed method in the sense of accuracy and CPU time.