| 热传导(对流-扩散)方程源项识别的粒子群优化算法 |
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| 引用本文： | 袁利国,邱华,聂笃宪.热传导(对流-扩散)方程源项识别的粒子群优化算法[J].数学的实践与认识,2009,39(14). |
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| 作者姓名： | 袁利国 邱华 聂笃宪 |
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| 作者单位： | 华南农业大学,数学系,广东,广州,510642 |
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| 基金项目： | 国家青年基金，华南农业大学校长基金 |
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| 摘 要： | 提出了利用粒子群优化(PSO)算法反演热传导方程与对流-扩散方程源项的一种新方法,在已有文献方法的基础上,求解出这两类方程正问题的解析解,再把源项识别问题转化为最优化问题,结合粒子群优化算法寻优求解.通过数值模拟与统计检验,结果表明,此方法可快速有效地实现热传导方程与对流-扩散方程源项的识别,并可推广应用到其它数学物理方程的源项或参数的反演识别.
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| 关 键 词： | 热传导方程 对流-扩散方程 稳恒源项 粒子群优化算法 统计检验 |
Source Term Identification of Heat Conduction (Convection-diffusion)Equation by Particle Swarm Optimization Algorithm |
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| YUAN Li-guo,QIU Hua,NIE Du-xian.Source Term Identification of Heat Conduction (Convection-diffusion)Equation by Particle Swarm Optimization Algorithm[J].Mathematics in Practice and Theory,2009,39(14). |
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| Authors: | YUAN Li-guo QIU Hua NIE Du-xian |
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| Abstract: | A new approach based on particle swarm optimization algorithm for stable source term identification of heat conduction(convection-diffusion) equation is proposed.First,we got the analytic solution of the equations with the methods in bibliography.Then,it transforms the source identicication problem into the solution of an optimization problem and find the optimal solution with particle swarm optimization(PSO) algorithm.With numerical simulation and statistical test,the results display that this method can find the source term of heat conduction(convection-diffusion) equation quickly and efficiently.This method can be popularized to solve inverse problem of source term identicication or parameter identification of mathematical physics equation. |
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| Keywords: | heat conduction equation convection-diffusion equation stable source term particle swarm optimization algorithm statistical test |
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