Open AccessA NEW NUMERICAL METHOD TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
Author(s) -
Jinjiao Hou,
Ning Jing,
Welreach Ngolo
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.12923
Subject(s) - mathematics , nonlinear system , kernel (algebra) , convergence (economics) , homotopy analysis method , fredholm integral equation , numerical analysis , integral equation , fredholm theory , mathematical analysis , homotopy , discrete mathematics , pure mathematics , physics , quantum mechanics , economics , economic growth
In this paper, a new method combining the simplified reproducing kernel method (SRKM) and the homotopy perturbation method (HPM) to solve the nonlinear Volterra-Fredholm integro-differential equations (V-FIDE) is proposed. Firstly the HPM can convert nonlinear problems into linear problems. After that we use the SRKM to solve the linear problems. Secondly, we prove the uniform convergence of the approximate solution. Finally, some numerical calculations are proposed to verify the effectiveness of the approach.