A new reproducing kernel method with higher convergence order for solving a Volterra–Fredholm integral equation

2020 ◽  
Vol 102 ◽  
pp. 106117 ◽  
Author(s):  
Hong Du ◽  
Zhong Chen
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Convergence Order ◽  
Reproducing Kernel Method

scholarly journals A high order approach for nonlinear Volterra-Hammerstein integral equations

2021 ◽  
Vol 7 (1) ◽  
pp. 1460-1469
Author(s):  
Jian Zhang ◽  
◽  
Jinjiao Hou ◽  
Jing Niu ◽  
Ruifeng Xie ◽  
...  
Keyword(s):  
Integral Equation ◽  
Nonlinear Integral Equation ◽  
Homotopy Perturbation Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Linear Equations ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Hammerstein Integral Equations ◽  
Homotopy Perturbation

<abstract><p>Here a scheme for solving the nonlinear integral equation of Volterra-Hammerstein type is given. We combine the related theories of homotopy perturbation method (HPM) with the simplified reproducing kernel method (SRKM). The nonlinear system can be transformed into linear equations by utilizing HPM. Based on the SRKM, we can solve these linear equations. Furthermore, we discuss convergence and error analysis of the HPM-SRKM. Finally, the feasibility of this method is verified by numerical examples.</p></abstract>

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