Haar wavelet quasilinearization method for solving nonlinear Troesch’s and Bratu’s problems

Document Type : Original Paper

Authors

1 Department of Mathematics, University of Mohaghegh Ardabili,Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabil, Iran.

2 Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabil, Iran.

Abstract

In this paper, we present a numerical method for solving nonlinear Troesch’s and Bratu’s problems. Quasilinearization process together with Haar wavelet approximation are employed to convert a nonlinear problem intoa set of linear algebraic equations. Several examples are given. We compare obtained computational results with available numerical and exact solutions found in the literature. Also numerical results are given in tables and figures and it is shown that the Haar wavelet quasilinearization (HWQ)approach is very attractive, convenient and effective.

Keywords

Main Subjects

References

,QWKLVSDSHUZHSUHVHQWDQXPHULFDOPHWKRGIRUVROYLQJQRQOLQHDU7URHVFK¶V DQG %UDWX¶V SUREOHPV
,Q WKLV PHWKRG ZH ZLOO XVH WKH TXDVLOLQHDUL]DWLRQ SURFHVVDQGWKH+DDUZDYHOHW EDVLV IXQFWLRQWRFRQYHUW QRQOLQHDU SUREOHPV LQWRDVHWRIOLQHDUDOJHEUDLFHTXDWLRQVYHUDOH[DPSOHVDUHJLYHQ DQGZHZLOO FRPSDUH
WKH REWDLQHG QXPHULFDO UHVXOWV ZLWK WKH UHVXOWV RI DQDO\WLFDO DQG QXPHULFDOPHWKRGVLQWKHOLWHUDWXUH
OVRQXPHULFDOUHVXOWVDUHJLYHQLQWDEOHV
DQGILJXUHVDQGLWLVVKRZQWKDWWKH+DDUZDYHOHWTXDVLOLQHDUL]DWLRQ DSSURDFKLVYHU\DWWUDFWLYHFRQYHQLHQWDQGHIIHFWLYH
Journal of Advanced Mathematical Modeling
Volume 7, Issue 2
April 2018
Pages 85-102

Files

History

  • Receive Date: 06 August 2016
  • Revise Date: 17 March 2018
  • Accept Date: 11 November 2017

Share

How to cite

Statistics