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Non-local Boundary Value Problem for Cauchy Problem for Laplace Equation in System of Polar Coordinates

Author: MuXiaoWei
Tutor: ChengJin
School: Fudan University
Course: Computational Mathematics
Keywords: non-local regularization Laplace annulus BEM polar coordinate
CLC: O175.8
Type: Master's thesis
Year: 2010
Downloads: 26
Quote: 0
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Abstract


In this thesis, we discuss the Cauchy problem for Laplace equation in system of polar coordinates,i.e.use the values of the function and its normal derivative in the outer boundary to compute the value of function in the inner boundary. Obviously,the problem is ill-posed,so we need regularization.The Auxiliary Boundary Condition method(ABC method) or non-local regularization method is used in this thesis.First,we obtain theo-retical results.And then perform our numerical tests to check the accuracy of our results.In Chapter l,we introduce the background of the research of Cauchy problem and the main methods and results of "differential" regularization.In Chapter 3,we use separation of variables to obtain the representation of the exact solution and the regularization solution for Laplace equation in 2D and 3D.By using this,we obtain the error estimates.In Chapter 4,we introduce the basic thought of BEM and its advantages and dis-advantages.Then,we present the main steps of BEM. Finally,we use matlab to perform our numerical tests and plot figures to compare.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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