...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Fuzzy sets and systems >On fuzzy solutions for partial differential equations
【24h】

On fuzzy solutions for partial differential equations

机译：偏微分方程的模糊解

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this study we investigate heat, wave and Poisson equations as classical models of partial differential equations (PDEs) with uncertain parameters, considering the parameters as fuzzy numbers. The fuzzy solution is built from fuzzification of the deterministic solution. The continuity of the Zadeh extension is used to obtain qualitative properties on regular α-cuts of the fuzzy solution. We prove the stability with respect to the initial boundary data, and show that as time goes to zero, the diameter of the fuzzy solution converges to zero and, as a consequence, to the cylindrical surface determined by the curve of the degree of membership. Numerical simulations are used to obtain a graphical representation of the fuzzy solution and a defuzzification of this solution is obtained using the center of gravity method. We theoretically show that the surface obtained by defuzzification with the plane determined by fixing time is indeed the solution of the same initial boundary problem for this time-point for the heat and Poisson equations and, in a particular case, for the wave equation. The deterministic solution and the defuzzified surface intercept are numerically compared using the Euclidean distance.
机译：在这项研究中，我们将热，波动和泊松方程作为具有不确定参数的偏微分方程（PDE）的经典模型进行研究，考虑参数为模糊数。模糊解决方案是基于确定性解决方案的模糊化而构建的。 Zadeh扩展的连续性用于获得模糊解的规则α割的定性性质。我们证明了相对于初始边界数据的稳定性，并表明随着时间趋于零，模糊解的直径收敛到零，结果收敛到由隶属度曲线确定的圆柱表面。数值模拟用于获得模糊解的图形表示，并使用重心方法对该解解模糊。从理论上讲，对于热和泊松方程，在特定情况下，对于波动方程，在固定时间确定的平面上进行去模糊处理而获得的表面确实是相同初始边界问题的解决方案。使用欧几里德距离对确定性解和去模糊化的表面截距进行数值比较。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号