# Solution of second order quasi-linear boundary value problems by a wavelet method

## Abstract

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.

- Authors:

- Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou (China)

- Publication Date:

- OSTI Identifier:
- 22391094

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ANALYTICAL SOLUTION; BENDING; BOUNDARY-VALUE PROBLEMS; COMPARATIVE EVALUATIONS; CONVERGENCE; EFFICIENCY; EXPANSION; NONLINEAR PROBLEMS; THERMAL CONDUCTION

### Citation Formats

```
Zhang, Lei, Zhou, Youhe, and Wang, Jizeng, E-mail: jzwang@lzu.edu.cn.
```*Solution of second order quasi-linear boundary value problems by a wavelet method*. United States: N. p., 2015.
Web. doi:10.1063/1.4912696.

```
Zhang, Lei, Zhou, Youhe, & Wang, Jizeng, E-mail: jzwang@lzu.edu.cn.
```*Solution of second order quasi-linear boundary value problems by a wavelet method*. United States. doi:10.1063/1.4912696.

```
Zhang, Lei, Zhou, Youhe, and Wang, Jizeng, E-mail: jzwang@lzu.edu.cn. Tue .
"Solution of second order quasi-linear boundary value problems by a wavelet method". United States.
doi:10.1063/1.4912696.
```

```
@article{osti_22391094,
```

title = {Solution of second order quasi-linear boundary value problems by a wavelet method},

author = {Zhang, Lei and Zhou, Youhe and Wang, Jizeng, E-mail: jzwang@lzu.edu.cn},

abstractNote = {A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.},

doi = {10.1063/1.4912696},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1648,

place = {United States},

year = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4912696

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