Meshless local radial point interpolation (MLRPI) for generalized telegraph and heat diffusion equation with non-local boundary conditions

• Autorzy: Shivanian E. , Khodayari A.

Identyfikatory

DOI

10.15632/jtam-pl.55.2.571

• Języki publikacji: EN

Abstrakty

EN

In this paper, the meshless local radial point interpolation (MLRPI) method is formulated to the generalized one-dimensional linear telegraph and heat diffusion equation with non-local boundary conditions. The MLRPI method is categorized under meshless methods in which any background integration cells are not required, so that all integrations are carried out locally over small quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. A technique based on the radial point interpolation is adopted to construct shape functions, also called basis functions, using the radial basis functions. These shape functions have delta function property in the frame work of interpolation, therefore they convince us to impose boundary conditions directly. The time derivatives are approximated by the finite difference time- -stepping method. We also apply Simpson’s integration rule to treat the non-local boundary conditions. Convergency and stability of the MLRPI method are clarified by surveying some numerical experiments.

Słowa kluczowe

EN

non-local boundary condition; meshless local radial point interpolation (MLRPI) method; local weak formulation; radial basis function; telegraph equation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2017
• Tom: Vol. 55 nr 2
• Strony: 571—582
• Opis fizyczny: Bibliogr. 37 poz., rys., tab.

Twórcy

autor

Shivanian E.

• Imam Khomeini International University, Department of Mathematics, Qazvin, Iran

autor

Khodayari A.

• Imam Khomeini International University, Department of Mathematics, Qazvin, Iran

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)