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
Citation: 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

High Accuracy Eigensolution and Its Extrapolation for Potential Equations

doi: 10.3879/j.issn.1000-0887.2010.12.005
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-11-05
  • Publish Date: 2010-12-15
  • 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.
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