| 数值求解一类空间分数阶扩散方程源项系数反问题 |
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| 引用本文： | 阮周生,张文,王泽文.数值求解一类空间分数阶扩散方程源项系数反问题[J].河北大学学报(自然科学版),2012,32(5):458-463. |
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| 作者姓名： | 阮周生 张文 王泽文 |
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| 作者单位： | 1. 东华理工大学 放射性地质与勘探技术国防重点学科实验室,江西抚州344000;东华理工大学理学院,江西南昌330013
2. 东华理工大学理学院,江西南昌,330013 |
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| 基金项目： | 国家自然科学基金资助项目(41001320,11161002);江西省自然科学基金资助项目(2009GZS0001);江西省教育厅科技资助项目(GJJ11151);放射性地质与勘探技术国防重点学科实验室资助项目(2010RGET12) |
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| 摘 要： | 数值求解一类空间分数阶扩散方程源项系数反问题.利用函数变换,将源项系数反问题转为对应的定解问题,利用隐式差分格式,求解对应定解问题,然后利用数值积分,求得待定系数函数的数值解,并且证明了隐式差分格式的绝对稳定性.通过数值算例表明,该数值方法具有较高的计算精度.
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| 关 键 词： | 反常扩散 空间分数阶导数 反问题 有限差分格式 稳定性 |
Numerical solution of source terms coefficient inverse problem for a kind of space fractional diffusion equation |
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| RUAN Zhousheng
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ZHANG Wen
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WANG Zewen.Numerical solution of source terms coefficient inverse problem for a kind of space fractional diffusion equation[J].Journal of Hebei University (Natural Science Edition),2012,32(5):458-463. |
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| Authors: | RUAN Zhousheng ZHANG Wen WANG Zewen |
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| Institution: | 1.Key Laboratory of Radioactive Geology and Exploration Technology Fundamental Science for National Defense,East China Institute of Technology,Fuzhou 344000,China;2.College of Science,East China Institute of Technology,Nanchang 330013,China) |
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| Abstract: | A numerical method for source coefficient inverse problem of a kind of one-dimensional space fractional diffusion equation is concerned.The inverse problem of source coefficient is converted to the corresponding definite problem through function transformation.Applying the implicit difference,the solution of the corresponding definite problem is founded.Using the numerical integral,the numerical solution of the undetermined function is founded,and the unconditional stability of difference scheme is proved.The numerical example shows that the proposed method has high accuracy. |
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| Keywords: | anomalous diffusion spatial fractional derivative inverse problem finite difference scheme stability |
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