Space–time localized polynomial basis functions for solving parabolic and hyperbolic equations
Journal
International Journal of Computer Mathematics
Date Issued
2021
Author(s)
Abstract
In this paper, two localized meshless schemes using polynomial basis functions have been presented for solving space–time problems. The proposed methods are especially attractive for solving time-dependent problems in 3D spacious domain. The results showed the simplicity and high accuracy of the proposed methods. Six numerical examples are given to illustrate the effectiveness of the proposed methods. We also presented the pros and cons of the proposed methods by comparing to the results of some recent publications using global polynomial basis functions and localized radial basis functions. ? 2021 Informa UK Limited, trading as Taylor & Francis Group.
Subjects
localized polynomial particular solutions
Polynomial
space–time problems
Hyperbolic functions
Numerical methods
Polynomials
Hyperbolic equations
Localised
Localized polynomial particular solution
Meshless
Parabolic Equations
Particular solution
Polynomial basis functions
Spacetime
Space–time problem
Time-dependent problem
Radial basis function networks
Type
journal article