| 一类抛物型方程反问题的数值解法 |
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| 引用本文： | 葛美宝,徐定华,王泽文,张文.一类抛物型方程反问题的数值解法[J].华东地质学院学报,2006,29(3):283-288. |
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| 作者姓名： | 葛美宝 徐定华 王泽文 张文 |
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| 作者单位： | 东华理工学院数学与信息科学学院 江西抚州344000 |
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| 摘 要： | 讨论了一类二阶抛物型方程反问题的数值解法。应用拟解法的思想,把原问题分解为一系列适定的正问题和一个不适定的线性代数方程组。对于相应的正问题,证明了解连续依赖于初始分布,由此得到了在时刻的稳定性估计。使用古典欧拉差分格式求解正问题和用截断奇异值分解法求解病态方程组。数值结果显示数值解与理论解吻合很好。
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| 关 键 词： | 抛物型方程 反问题 拟解法 数值解 |
| 文章编号： | 1000-2251(2006)03-283-06 |
| 收稿时间： | 2006-06-06 |
| 修稿时间： | 2006年6月6日 |
Numerical Method of an Inverse Problem for a Class of Parabolic Equation |
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| GE Mei-bao,XU Ding-hua,WANG Ze-wen,ZHANG Wen.Numerical Method of an Inverse Problem for a Class of Parabolic Equation[J].Journal of East China Geological Institute,2006,29(3):283-288. |
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| Authors: | GE Mei-bao XU Ding-hua WANG Ze-wen ZHANG Wen |
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| Institution: | Faculty of Mathematics and Information Science, East China Institute of Technology ,Fuzhou, JX 344000, China |
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| Abstract: | A method of solution of backward second-order parabolic equation problem is discussed in the article.The method employs a quasisolution approach and is based on the separation of the problem into a sequence of well-posed forward problems and an ill-posed system of algebraic equations.For the corresponding forward problem the continuous dependence of the solution on the initial data is proved.From this result a stability estimate on the final time T is obtained.Using the perform of classic Euler solves the forward problem the ill-conditioned system of algebraic equation is solved by using truncated singular value decomposition.The result manifests that the numerical solution and theoretical solution are well consistent. |
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| Keywords: | parabolic equations inverse problem quasisolution approach numerical method |
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