Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29644

Select areas to restrict search in scientific publication database:
Quasilinearization–Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem
In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Digital Object Identifier (DOI):


[1] S. Abbasbandy, E. Shivanian, Exact analytical solution of a nonlinear equation arising in heat transfer, Phys. Lett. A. 347 (2010) 567-574.
[2] M. H. Chang, A numerical analysis to the non-linear fin problem, Int. J. Heat. Mass. Tran. 48 (2005) 1819-1824.
[3] R. Cortell, A numerical analysis to the non-linear fin problem, J. Zhejiang. Univ-Sc. A. 9 (2008) 648-653.
[4] S. D. Conte, C. de Boor, Elementary numerical analysis, McGrow Hill, 1980.
[5] A. Ralston, P. Rabinowitz, A first course in numerical analysis, McGraw Hill, 1988.
[6] R. E. Bellman, R. E. Kalaba, Quasilinearization and nonlinear Boundaryvalue problems, Elsevier, New York, 1965.
[7] R. Kalaba, On nonlinear differential equations,the maximum operation and monotone convergence, J. Math. Mech. 8 (1968) 519-574.
[8] V. B. Mandelzweig, R. Krivec, Fast convergent quasilinearization approach to quantum problems, Aip. Conf. Proc. 768 (2005) 413-419.
[9] V. B. Mandelzweig, F. Tabakin, Quasilinearization approach to nonlinear problems in physics with application to nonlinear odes, Comput. Phys. Commun. 141 (2001) 268-281.
[10] J. I. Ramos, Piecewise quasilinearization techniques for singular boundary-value problems, Comput. Phys. Commun. 158 (2003) 12-25.
[11] V. B. Mandelzweig, Quasilinearization method: Nonperturbative approach to physical problems, Phys. Atom. Nucl+. 68 (2005) 1227-1258.
[12] V. B. Mandelzweig, Comparison of quasilinear and wkb approximations, Ann. Phys-New York. 321 (2006) 2810-2829.
[13] P. J. Davis, Interpolation and approximation, Dover, New York, 1975.
[14] G. M. Phillips, Interpolation and approximation by polynomials, Springer, New York, 2003.
[15] P. Henrici, Essentials of Numerical Analysis, Wiley, New York, 1982.
[16] H. Rutishauser, Vorlesungen ¨uber numerische Mathematik, Birkh¨auser, Boston, 1990.
[17] H. Salzer, Lagrangian interpolation at the chebyshev points xn,╬¢ ≡ cos(╬¢¤Ç/n), ╬¢ = 0(1)n; some unnoted advantages, Comput. J. 15 (1972) 156-159.
[18] W. Werner, Polynomial interpolation: Lagrange versus newton, Math. Comput. 43 (1984) 205-217.
[19] L. Winrich, Note on a comparison of evaluation schemes for the interpolating polynomial, Comput. J. 12 (1969) 154-155.
[20] J. Berrut, L. Trefethen, Barycentric lagrange interpolation, SIAM. Rev. 46 (2004) 501-517.
[21] N. J. Higham, The numerical stability of barycentric lagrange interpolation, Ima. J. Numer. Anal. 24 (2004) 547-556.
[22] J. A. Taylor, F. S. Hover, Economical simulation in particle filtering using interpolation, IEEE. Int. Conf. Info. Aut. (ICIA) (2009) 1326- 1330.
[23] P. J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975.
[24] S. Liaw, R. Yeh, Fins with temperature dependent surface heat fluxÔÇöi: Single heat transfer mode, Int. J. Heat. Mass. Tran. 37 (1994) 1509- 1515.
[25] S. Liaw, R. Yeh, Fins with temperature dependent surface heat fluxÔÇöii: Multi-boiling heat transfer, Int. J. Heat. Mass. Tran. 37 (1994) 1517- 1524.
[26] V. Lakshmikantham, A. S. Vatsala, Generalized Quasilinearization for Nonlinear Problems (Mathematics and Its Applications), Kluwer Academic, Dordrecht, 1998.
[27] M. N. Koleva, L. G. Vulkov, Two-grid quasilinearization approach to odes with applications to model problems in physics and mechanics, Comput. Phys. Commun. 181 (2010) 663-670.
[28] J. L. Lagrange, Lec┬©ons 'el'ementaires sur les math'ematiques, donn'ees `a lEcole Normale en1795, Oeuvres VII, GauthierVillars, Paris, 1877.
Vol:13 No:05 2019Vol:13 No:04 2019Vol:13 No:03 2019Vol:13 No:02 2019Vol:13 No:01 2019
Vol:12 No:12 2018Vol:12 No:11 2018Vol:12 No:10 2018Vol:12 No:09 2018Vol:12 No:08 2018Vol:12 No:07 2018Vol:12 No:06 2018Vol:12 No:05 2018Vol:12 No:04 2018Vol:12 No:03 2018Vol:12 No:02 2018Vol:12 No:01 2018
Vol:11 No:12 2017Vol:11 No:11 2017Vol:11 No:10 2017Vol:11 No:09 2017Vol:11 No:08 2017Vol:11 No:07 2017Vol:11 No:06 2017Vol:11 No:05 2017Vol:11 No:04 2017Vol:11 No:03 2017Vol:11 No:02 2017Vol:11 No:01 2017
Vol:10 No:12 2016Vol:10 No:11 2016Vol:10 No:10 2016Vol:10 No:09 2016Vol:10 No:08 2016Vol:10 No:07 2016Vol:10 No:06 2016Vol:10 No:05 2016Vol:10 No:04 2016Vol:10 No:03 2016Vol:10 No:02 2016Vol:10 No:01 2016
Vol:9 No:12 2015Vol:9 No:11 2015Vol:9 No:10 2015Vol:9 No:09 2015Vol:9 No:08 2015Vol:9 No:07 2015Vol:9 No:06 2015Vol:9 No:05 2015Vol:9 No:04 2015Vol:9 No:03 2015Vol:9 No:02 2015Vol:9 No:01 2015
Vol:8 No:12 2014Vol:8 No:11 2014Vol:8 No:10 2014Vol:8 No:09 2014Vol:8 No:08 2014Vol:8 No:07 2014Vol:8 No:06 2014Vol:8 No:05 2014Vol:8 No:04 2014Vol:8 No:03 2014Vol:8 No:02 2014Vol:8 No:01 2014
Vol:7 No:12 2013Vol:7 No:11 2013Vol:7 No:10 2013Vol:7 No:09 2013Vol:7 No:08 2013Vol:7 No:07 2013Vol:7 No:06 2013Vol:7 No:05 2013Vol:7 No:04 2013Vol:7 No:03 2013Vol:7 No:02 2013Vol:7 No:01 2013
Vol:6 No:12 2012Vol:6 No:11 2012Vol:6 No:10 2012Vol:6 No:09 2012Vol:6 No:08 2012Vol:6 No:07 2012Vol:6 No:06 2012Vol:6 No:05 2012Vol:6 No:04 2012Vol:6 No:03 2012Vol:6 No:02 2012Vol:6 No:01 2012
Vol:5 No:12 2011Vol:5 No:11 2011Vol:5 No:10 2011Vol:5 No:09 2011Vol:5 No:08 2011Vol:5 No:07 2011Vol:5 No:06 2011Vol:5 No:05 2011Vol:5 No:04 2011Vol:5 No:03 2011Vol:5 No:02 2011Vol:5 No:01 2011
Vol:4 No:12 2010Vol:4 No:11 2010Vol:4 No:10 2010Vol:4 No:09 2010Vol:4 No:08 2010Vol:4 No:07 2010Vol:4 No:06 2010Vol:4 No:05 2010Vol:4 No:04 2010Vol:4 No:03 2010Vol:4 No:02 2010Vol:4 No:01 2010
Vol:3 No:12 2009Vol:3 No:11 2009Vol:3 No:10 2009Vol:3 No:09 2009Vol:3 No:08 2009Vol:3 No:07 2009Vol:3 No:06 2009Vol:3 No:05 2009Vol:3 No:04 2009Vol:3 No:03 2009Vol:3 No:02 2009Vol:3 No:01 2009
Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007