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

Zarebnia, Mohammad; Barandak Imcheh, Hosein

doi:10.22055/jamm.2018.18862.1307

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

Document Type : Original Paper

Authors

Mohammad Zarebnia ¹

Hosein Barandak Imcheh ²

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.

10.22055/jamm.2018.18862.1307

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

Haar wavelet

Operational matrix

Quasilinearization

Troesch’s problem

Bratu’s problem

Subjects

Numerical Analysis

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