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A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs

Author

Listed:
  • Juan José Benito

    (Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Ángel García

    (Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Mihaela Negreanu

    (Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Francisco Ureña

    (Escuela Técnica de Ingenieros Industriales, Universidad Nacional de Educación a Distancia, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Antonio M. Vargas

    (Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Juan José Benito & Ángel García & Mihaela Negreanu & Francisco Ureña & Antonio M. Vargas, 2022. "A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1870-:d:827732
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    References listed on IDEAS

    as
    1. Nguyen, Vinh Phu & Rabczuk, Timon & Bordas, Stéphane & Duflot, Marc, 2008. "Meshless methods: A review and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 763-813.
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    Cited by:

    1. Francisco Ureña & Ángel García & Antonio M. Vargas, 2022. "Preface to “Applications of Partial Differential Equations in Engineering”," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

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