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Volume 34, Issue 3
Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems

Hao Wu

Commun. Math. Res., 34 (2018), pp. 278-288.

Published online: 2019-12

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  • Abstract

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

  • Keywords

Peridynamics, exponential convergence, nonlocal boundary value problem, analytic function, finite-dimensional approximation

  • AMS Subject Headings

45A05, 46N20, 65B10, 65M60, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hzw0010@auburn.edu (Hao Wu)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-278, author = {Hao and Wu and hzw0010@auburn.edu and 5957 and Department of Mathematics and Statistics, Auburn University, AL, 36830, US and Hao Wu}, title = {Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {3}, pages = {278--288}, abstract = {

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.03.09}, url = {http://global-sci.org/intro/article_detail/cmr/13494.html} }
TY - JOUR T1 - Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems AU - Wu , Hao JO - Communications in Mathematical Research VL - 3 SP - 278 EP - 288 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.03.09 UR - https://global-sci.org/intro/article_detail/cmr/13494.html KW - Peridynamics, exponential convergence, nonlocal boundary value problem, analytic function, finite-dimensional approximation AB -

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

Hao Wu. (2019). Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems. Communications in Mathematical Research . 34 (3). 278-288. doi:10.13447/j.1674-5647.2018.03.09
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