A new least‐squares‐based reproducing kernel method for solving regular and weakly singular Volterra‐Fredholm integral equations with smooth and nonsmooth solutions

2021 ◽  
Author(s):  
Minqiang Xu ◽  
Jing Niu ◽  
Emran Tohidi ◽  
Jinjiao Hou ◽  
Danhua Jiang
Keyword(s):  
Least Squares ◽  
Integral Equations ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Fredholm Integral Equations ◽  
Reproducing Kernel Method ◽  
Weakly Singular

scholarly journals The Combined Reproducing Kernel Method and Taylor Series for Solving Weakly Singular Fredholm Integral Equations

2016 ◽  
Vol 5 (3) ◽  
pp. 109
Author(s):  
Azizallah Alvandi ◽  
Mahmoud Paripour
Keyword(s):  
Integral Equations ◽  
Taylor Series ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Fredholm Integral Equations ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Reproducing Kernel Method ◽  
Weakly Singular ◽  
Reproducing Kernel Function

<p>In this paper, a numerical method is proposed for solving weakly singular Fredholm integral equations in Hilbert reproducing kernel space (RKHS). The Taylor series is used to remove singularity and reproducing kernel function are used as a basis. The effectiveness and stability of the numerical scheme is illustrated through two numerical examples.</p>

scholarly journals Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Li-Hong Yang ◽  
Hong-Ying Li ◽  
Jing-Ran Wang
Keyword(s):  
Integral Equations ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Numerical Technique ◽  
Volterra Integral Equations ◽  
Reproducing Kernel Space ◽  
Approximation Solution ◽  
Reproducing Kernel Method ◽  
Modified Method ◽  
Linear Volterra Integral Equations

A numerical technique based on reproducing kernel methods for the exact solution of linear Volterra integral equations system of the second kind is given. The traditional reproducing kernel method requests that operator a satisfied linear operator equationAu=f, is bounded and its image space is the reproducing kernel spaceW21[a,b]. It limits its application. Now, we modify the reproducing kernel method such that it can be more widely applicable. Then-term approximation solution obtained by the modified method is of high accuracy. The numerical example compared with other methods shows that the modified method is more efficient.

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