# Determining An Unknown Boundary Condition by An Iteration Method

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## Abstract

**:**

## 1. Introduction

- The reversed-time problem (RTP): $v(x,0)$ is unknown;
- the inverse boundary problem (IBP): the Dirichlet or Neumann condition is unknown;
- the inverse coefficient problem (ICP): ${a}_{1},{a}_{2}$, or ${a}_{3}$ is unknown; and
- the inverse heat source (sink) problem (IHSP): $F(x,t)$ is unknown.

## 2. Problem Statement

## 3. Analysis of VIM

## 4. Illustrative Examples

#### 4.1. Example 1

#### 4.2. Example 2

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

IPHCE | Inverse Problem of Heat Conduction Equation |

IBP | inverse boundary problem |

ICP | inverse coefficient problem |

IHSP | inverse heat source (sink) problem |

RTP | reversed-time problem |

VIM | variational iteration method |

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**MDPI and ACS Style**

Huang, D.; Li, Y.; Pei, D.
Determining An Unknown Boundary Condition by An Iteration Method. *Symmetry* **2018**, *10*, 409.
https://doi.org/10.3390/sym10090409

**AMA Style**

Huang D, Li Y, Pei D.
Determining An Unknown Boundary Condition by An Iteration Method. *Symmetry*. 2018; 10(9):409.
https://doi.org/10.3390/sym10090409

**Chicago/Turabian Style**

Huang, Dejian, Yanqing Li, and Donghe Pei.
2018. "Determining An Unknown Boundary Condition by An Iteration Method" *Symmetry* 10, no. 9: 409.
https://doi.org/10.3390/sym10090409