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A Note on Numerical Solution of Classical Darboux Problem
  • Kotapally Kumar
Kotapally Kumar
IIT Roorkee
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Abstract

Recently, many authors studied the numerical solution of the classical Darboux problem in its integral form via a two-dimensional nonlinear Volterra-Fredholm integral equation. In the present article, a numerical technique based on the Chebyshev wavelet is proposed to solve the Darboux problem directly without converting into a nonlinear Volterra-Fredholm integral equation. The proposed technique is different from the techniques discussed in [1, 2, 4, 7, 11, 16, 17, 18, 19]. The proposed approach produces higher accuracy than its counterpart techniques. The proposed scheme illustrated with suitable examples to show the advantages in terms of its accuracy with lesser grid size.

Peer review status:ACCEPTED

21 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
26 Jun 2020Submission Checks Completed
26 Jun 2020Assigned to Editor
29 Jun 2020Reviewer(s) Assigned
21 Dec 2020Review(s) Completed, Editorial Evaluation Pending
22 Dec 2020Editorial Decision: Revise Major
09 Feb 20211st Revision Received
09 Feb 2021Submission Checks Completed
09 Feb 2021Assigned to Editor
11 Feb 2021Reviewer(s) Assigned
22 May 2021Review(s) Completed, Editorial Evaluation Pending
23 May 2021Editorial Decision: Accept