High Accuracy Eigensolution and Its Extrapolation for Potential Equations

CHENG Pan; HUANG Jin; ZENG Guang

doi:10.3879/j.issn.1000-0887.2010.12.005

Volume 31 Issue 12

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CHENG Pan, HUANG Jin, ZENG Guang. High Accuracy Eigensolution and Its Extrapolation for Potential Equations[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1445-1453. doi: 10.3879/j.issn.1000-0887.2010.12.005

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High Accuracy Eigensolution and Its Extrapolation for Potential Equations

doi: 10.3879/j.issn.1000-0887.2010.12.005

School of Mathematical Science, University of Electronic Science & Technology of China, Chengdu 611731, P. R. China;
School of Science, Chongqing Jiaotong University, Chongqing 400074, P. R. China

Received Date: 1900-01-01
Rev Recd Date: 2010-11-05
Publish Date: 2010-12-15

Abstract

Abstract

By the potential theorem,fundamental boundary eigenproblems were converted into boundary in tegral equations (BIE) with logarithmic singularity.Mechanical quadrature methods (MQMs) were presented to obtain eigen solutions which were used to solve Laplace's equations.And the MQMs possess high accuracies and low computing complexities.The convergence and stability were proved based on Anselone's collective compact and asymptotical compact theory.Furthermore,an asymptotic expansion with odd powers of the errors is presented.Using h³-Richardson extrapolation algorithm (EA),the accuracy order of the approximation can be greatly improved,and a posterior error estmiate can be obtained as the self-adaptive algorithms.The efficiency of the algorithm is illustrated by examples.
- potential equation,
- mechanical quadrature methods,
- Richard sonextrapolation,
- posteriori error estimate

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References(14)

References

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