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Title: Application of multiquadric method for numerical solution of elliptic partial differential equations

Abstract

We have used the multiquadric (MQ) approximation scheme for the solution of elliptic partial differential equations with Dirichlet and/or Neumann boundary conditions. The scheme has the advantage to use the data points in arbitrary locations with an arbitrary ordering. Two dimensional Laplace, Poisson and Biharmonic equations describing the various physical processes, have been taken as the test examples. The agreement is found to be very good between the computed and exact solutions. The method also provides an excellent approximation with curve boundary.

Authors:
 [1];  [2];  [3]
  1. Indian Inst. of Tech., New Delhi (India)
  2. Lawrence Livermore National Lab., CA (United States)
  3. Govt. Girls Sr. Sec. School I, Madangir, New Delhi (India)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10156506
Report Number(s):
UCRL-CR-115793
ON: DE94012999
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Jan 1994
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARTIAL DIFFERENTIAL EQUATIONS; NUMERICAL SOLUTION; DIRICHLET PROBLEM; POISSON EQUATION; LAPLACE EQUATION; ITERATIVE METHODS; 990200; MATHEMATICS AND COMPUTERS

Citation Formats

Sharan, M, Kansa, E J, and Gupta, S. Application of multiquadric method for numerical solution of elliptic partial differential equations. United States: N. p., 1994. Web. doi:10.2172/10156506.
Sharan, M, Kansa, E J, & Gupta, S. Application of multiquadric method for numerical solution of elliptic partial differential equations. United States. https://doi.org/10.2172/10156506
Sharan, M, Kansa, E J, and Gupta, S. 1994. "Application of multiquadric method for numerical solution of elliptic partial differential equations". United States. https://doi.org/10.2172/10156506. https://www.osti.gov/servlets/purl/10156506.
@article{osti_10156506,
title = {Application of multiquadric method for numerical solution of elliptic partial differential equations},
author = {Sharan, M and Kansa, E J and Gupta, S},
abstractNote = {We have used the multiquadric (MQ) approximation scheme for the solution of elliptic partial differential equations with Dirichlet and/or Neumann boundary conditions. The scheme has the advantage to use the data points in arbitrary locations with an arbitrary ordering. Two dimensional Laplace, Poisson and Biharmonic equations describing the various physical processes, have been taken as the test examples. The agreement is found to be very good between the computed and exact solutions. The method also provides an excellent approximation with curve boundary.},
doi = {10.2172/10156506},
url = {https://www.osti.gov/biblio/10156506}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Jan 01 00:00:00 EST 1994},
month = {Sat Jan 01 00:00:00 EST 1994}
}