An Improved Approach for Solving Partial Differential Equation Based on Reproducing Kernel Method | Zendy

Ming-Jing Du | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

An Improved Approach for Solving Partial Differential Equation Based on Reproducing Kernel Method

Author(s) -

Ming-Jing Du

Publication year - 2021

Publication title -

security and communication networks

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.446

H-Index - 43

eISSN - 1939-0114

pISSN - 1939-0122

DOI - 10.1155/2021/7741274

Subject(s) - kernel (algebra) , piecewise , partial differential equation , interpolation (computer graphics) , mathematics , representer theorem , computer science , kernel method , differential equation , series (stratigraphy) , mathematical optimization , kernel embedding of distributions , mathematical analysis , artificial intelligence , motion (physics) , paleontology , combinatorics , support vector machine , biology

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research