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Hybrid Methods in Engineering

ISSN Print: 1099-2391
ISSN Online: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v3.i1.70
6 pages

CONVERGENCE ACCELERATION OF INTEGRAL TRANSFORM SOLUTIONS

Mikhail D. Mikhailov
Applied Mathematics Center, PO Box 384, Sofia, Technical University, Sofia, Bulgaria; and Mechanical Engineering Department—EE/COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68.503, Rio de Janeiro, RJ, 21945-970, Brasil
Renato M. Cotta
Laboratory of Nano- and Microfluidics and Microsystems, LabMEMS, Mechanical Engineering Department and Nanotechnology Engineering Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, Cx. Postal 68503, Rio de Janeiro, RJ, CEP 21945-970, Brazil; Interdisciplinary Nucleus for Social Development—NIDES/CT, UFRJ, Brazil; Mechanical Engineering Department, University College London, UCL, United Kingdom

ABSTRACT

A number of techniques, intended to accelerate convergence of eigenseries solution, are investigated. The test problem describes transient temperature distribution along fins of constant profile. The solutions are presented in a form that permitted to work with time independent functions. For any solution are used as many terms as necessary to obtain 5 significant digits. It is shown that the splitting-up solution offers ideal convergence in contrast to the slowly convergent classical integral transform solution. The convergence of single filter solution, double filter solution, integral balance solution, and combined filtering and integral balance solution are acceptable for practical applications. It is demonstrated that the Shanks transformation may considerably accelerate the convergence of eigenseries solution.


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