A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs

Juan José Benito, Ángel García, Mihaela Negreanu, Francisco Ureña and Antonio M. Vargas
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Juan José Benito: Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
Ángel García: Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
Mihaela Negreanu: Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
Francisco Ureña: Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
Antonio M. Vargas: Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain

Mathematics, 2022, vol. 10, issue 11, 1-12

Abstract: We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear parabolic PDEs. The method is based on a moving least squares method, more precisely, the generalized finite difference method (GFDM), which allows us to select well-conditioned stars. Several 2D and 3D examples, including the time variable, are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time.

Keywords: generalized finite differences; meshless method; parabolic partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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