Chen C.SNaji ACao YChen C.-S.CHUIN-SHAN CHEN2022-03-222022-03-22202100207160https://www.scopus.com/inward/record.uri?eid=2-s2.0-85119672724&doi=10.1080%2f00207160.2021.2000968&partnerID=40&md5=08a82d5e5fc5cbf578c46296cfebfebchttps://scholars.lib.ntu.edu.tw/handle/123456789/598421In 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.localized polynomial particular solutionsPolynomialspace–time problemsHyperbolic functionsNumerical methodsPolynomialsHyperbolic equationsLocalisedLocalized polynomial particular solutionMeshlessParabolic EquationsParticular solutionPolynomial basis functionsSpacetimeSpace–time problemTime-dependent problemRadial basis function networksjournal article10.1080/00207160.2021.20009682-s2.0-85119672724