### Abstract

A new technique using an adaptive fuzzy algorithm to obtain the solution of "Heat Conduction Equation" (HCE) is presented. The design objective is to find one fuzzy solution to satisfy precisely the "Heat Conduction Equation" encountered in practical application and the initial/boundary conditions. According to the concept of fuzzy logic systems, a rough fuzzy solution with adjustable parameters for the "Heat Conduction Equation" is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been proven. Furthermore, the error equations in mesh points are also proven to converge to zero for the "Heat Conduction Equation" with one sufficient condition. As the above mentions, our design objective is to treat the solution finding problem of the "Heat Conduction Equation" with a really new fuzzy approach concept.

Original language | English |
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Pages (from-to) | 863-867 |

Number of pages | 5 |

Journal | Advanced Science Letters |

Volume | 8 |

DOIs | |

Publication status | Published - 2012 Aug 2 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Health(social science)
- Mathematics(all)
- Education
- Environmental Science(all)
- Engineering(all)
- Energy(all)

### Cite this

*Advanced Science Letters*,

*8*, 863-867. https://doi.org/10.1166/asl.2012.2383

}

*Advanced Science Letters*, vol. 8, pp. 863-867. https://doi.org/10.1166/asl.2012.2383

**An advanced solution design for Heat Conduction Equation : Adaptive fuzzy approach.** / Chen, Yung-Yu; Chang, Shyang Jye.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An advanced solution design for Heat Conduction Equation

T2 - Adaptive fuzzy approach

AU - Chen, Yung-Yu

AU - Chang, Shyang Jye

PY - 2012/8/2

Y1 - 2012/8/2

N2 - A new technique using an adaptive fuzzy algorithm to obtain the solution of "Heat Conduction Equation" (HCE) is presented. The design objective is to find one fuzzy solution to satisfy precisely the "Heat Conduction Equation" encountered in practical application and the initial/boundary conditions. According to the concept of fuzzy logic systems, a rough fuzzy solution with adjustable parameters for the "Heat Conduction Equation" is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been proven. Furthermore, the error equations in mesh points are also proven to converge to zero for the "Heat Conduction Equation" with one sufficient condition. As the above mentions, our design objective is to treat the solution finding problem of the "Heat Conduction Equation" with a really new fuzzy approach concept.

AB - A new technique using an adaptive fuzzy algorithm to obtain the solution of "Heat Conduction Equation" (HCE) is presented. The design objective is to find one fuzzy solution to satisfy precisely the "Heat Conduction Equation" encountered in practical application and the initial/boundary conditions. According to the concept of fuzzy logic systems, a rough fuzzy solution with adjustable parameters for the "Heat Conduction Equation" is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been proven. Furthermore, the error equations in mesh points are also proven to converge to zero for the "Heat Conduction Equation" with one sufficient condition. As the above mentions, our design objective is to treat the solution finding problem of the "Heat Conduction Equation" with a really new fuzzy approach concept.

UR - http://www.scopus.com/inward/record.url?scp=84864384681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864384681&partnerID=8YFLogxK

U2 - 10.1166/asl.2012.2383

DO - 10.1166/asl.2012.2383

M3 - Article

VL - 8

SP - 863

EP - 867

JO - Advanced Science Letters

JF - Advanced Science Letters

SN - 1936-6612

ER -