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Chin. Phys. B, 2010, Vol. 19(1): 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

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
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.
Keywords:  control parameter      diffusion processes      temperature overspecification      quasi-interpolation  
Received:  07 February 2009      Revised:  23 April 2009      Accepted manuscript online: 
PACS:  05.60.-k (Transport processes)  
  02.30.Jr (Partial differential equations)  
  02.30.Yy (Control theory)  
  02.60.Ed (Interpolation; curve fitting)  
Fund: 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).

Cite this article: 

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 2010 Chin. Phys. B 19 010201

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