Premium
Numerical scheme for solving system of fractional partial differential equations with Volterra‐type integral term through two‐dimensional block‐pulse functions
Author(s) -
Xie Jiaquan,
Ren Zhongkai,
Li Yugui,
Wang Xiaogang,
Wang Tao
Publication year - 2019
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.22383
Subject(s) - mathematics , volterra integral equation , fractional calculus , algebraic equation , convergence (economics) , block (permutation group theory) , partial differential equation , scheme (mathematics) , type (biology) , integral equation , mathematical analysis , nonlinear system , ecology , biology , physics , geometry , quantum mechanics , economic growth , economics
In the current study, an approximate scheme is established for solving the fractional partial differential equations (FPDEs) with Volterra integral terms via two‐dimensional block‐pulse functions (2D‐BPFs). According to the definitions and properties of 2D‐BPFs, the original problem is transformed into a system of linear algebra equations. By dispersing the unknown variables for these algebraic equations, the numerical solutions can be obtained. Besides, the proof of the convergence of this system is given. Finally, several numerical experiments are presented to test the feasibility and effectiveness of the proposed method.