Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method

doi:10.1088/1674-1056/19/1/010201

中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10201-010201.doi: 10.1088/1674-1056/19/1/010201

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Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method

马利敏, 吴宗敏

Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

收稿日期:2009-02-07 修回日期:2009-04-23 出版日期:2010-01-15 发布日期:2010-01-15
基金资助:
Project supported by the National Key Basic Research Program of China (Grant No. 2006CB303102) and Science and Technology Commission of Shanghai Municipality, China (Grant No. 09DZ2272900).

Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method

Ma Li-Min(马利敏) and Wu Zong-Min(吴宗敏)

Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received:2009-02-07 Revised:2009-04-23 Online:2010-01-15 Published:2010-01-15
Supported by:
Project supported by the National Key Basic Research Program of China (Grant No. 2006CB303102) and Science and Technology Commission of Shanghai Municipality, China (Grant No. 09DZ2272900).

摘要/Abstract

摘要： In this paper, we use a kind of univariate multiquadric quasi-interpolation to solve a parabolic equation with overspecified data, which has arisen in many physical phenomena. We obtain the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a simple forward difference to approximate the temporal derivative of the dependent variable. The advantage of the presented scheme is that the algorithm is very simple so it is very easy to implement. The results of the numerical experiment are presented and are compared with the exact solution to confirm the good accuracy of the presented scheme.

Abstract: In this paper, we use a kind of univariate multiquadric quasi-interpolation to solve a parabolic equation with overspecified data, which has arisen in many physical phenomena. We obtain the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a simple forward difference to approximate the temporal derivative of the dependent variable. The advantage of the presented scheme is that the algorithm is very simple so it is very easy to implement. The results of the numerical experiment are presented and are compared with the exact solution to confirm the good accuracy of the presented scheme.

Key words: control parameter, diffusion processes, temperature overspecification, quasi-interpolation

中图分类号: (Transport processes)

05.60.-k

02.30.Jr (Partial differential equations) 02.30.Yy (Control theory) 02.60.Ed (Interpolation; curve fitting)

马利敏, 吴宗敏. Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method[J]. 中国物理B, 2010, 19(1): 10201-010201.

Ma Li-Min(马利敏) and Wu Zong-Min(吴宗敏). Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method[J]. Chin. Phys. B, 2010, 19(1): 10201-010201.

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Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method

Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method

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