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A new least square based reproducing kernel space method for solving regular and weakly singular 1D Volterra-Fredholm integral equations with smooth and nonsmooth solutions
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  • Minqiang Xu,
  • Jing Niu,
  • Emran Tohidi,
  • Jinjiao Hou
Minqiang Xu
Zhejiang University of Technology

Corresponding Author:[email protected]

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Jing Niu
Harbin Normal University
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Emran Tohidi
Ton Duc Thang University
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Jinjiao Hou
Harbin Normal University - Songbei Campus
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Based on the least square method, we proposed a new algorithm to obtain the solution of the second kind regular and weakly singular Volterra-Fredholm integral equations in reproducing kernel spaces. The stability and uniform convergence of the algorithm are investigated in details. Numerical experiments verify the theoretical findings. Meanwhile this method is also applicable to the nonlinear Volterra integral equations. Test problems which have non-smooth solutions are also considered and our proposed method is efficient as some recent Krylov subspace methods such as LSQR and LSMR.
10 Aug 2020Submitted to Mathematical Methods in the Applied Sciences
11 Aug 2020Submission Checks Completed
11 Aug 2020Assigned to Editor
16 Aug 2020Reviewer(s) Assigned
20 Feb 2021Review(s) Completed, Editorial Evaluation Pending
05 Mar 2021Editorial Decision: Revise Minor
17 Mar 20211st Revision Received
17 Mar 2021Submission Checks Completed
17 Mar 2021Assigned to Editor
17 Mar 2021Editorial Decision: Accept
11 May 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7444