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Compact finite difference scheme for the solution of a time fractional partial integro‐differential equation with a weakly singular kernel
Author(s) -
Mohebbi Akbar
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4549
Subject(s) - mathematics , convergence (economics) , kernel (algebra) , partial differential equation , stability (learning theory) , mathematical analysis , fractional calculus , scheme (mathematics) , integro differential equation , order (exchange) , first order partial differential equation , pure mathematics , finance , machine learning , computer science , economics , economic growth
In this paper, we develop a high‐order finite difference scheme for the solution of a time fractional partial integro‐differential equation with a weakly singular kernel. The fractional derivative is used in the Riemann‐Liouville sense. We prove the unconditional stability and convergence of scheme using energy method and show that the convergence order is O ( τ + h 4 ) . We provide some numerical experiments to confirm the efficiency of suggested scheme. The results of numerical experiments are compared with analytical solutions to show the efficiency of proposed scheme. It is illustrated that the numerical results are in good agreement with theoretical ones.