An Improved Approach for Solving Partial Differential Equation Based on Reproducing Kernel Method. (30th November 2021)

• Record Type: Journal Article
• Authors: Du, Mingjing
• Other Names: Zhong Joni Academic Editor.
• Is Part Of: Security and communication networks. Volume 2021(2021)
• Publication Date: 2021-11-30
• Subjects: Computer networks -- Security measures -- Periodicals; Computer security -- Periodicals; Cryptography -- Periodicals; 005.805
• DOI: 10.1155/2021/7741274
• Languages: English
• ISSNs: 1939-0114

Abstract

Abstract : The traditional reproducing kernel method (TRKM) cannot obtain satisfactory numerical results for solving the partial differential equation (PDE). In this study, for the first time, the abovementioned problems are solved by adaptive piecewise interpolation reproducing kernel method (APIRKM) to obtain the exact and approximate solutions of partial differential equations by means of series expansion using reconstructed kernel function. The highlight of this paper is to obtain more accurate approximate solution and save more time through adaptive discovery. Numerical solutions of the three examples show that the present method is more advantageous than TRKM.