CHENG Pan, HUANG Jin, WANG Zhu. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1405-1414. doi: 10.3879/j.issn.1000-0887.2011.12.002
 Citation: CHENG Pan, HUANG Jin, WANG Zhu. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1405-1414.

Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation

doi: 10.3879/j.issn.1000-0887.2011.12.002
• Received Date: 2010-11-18
• Rev Recd Date: 2011-11-02
• Publish Date: 2011-12-15
• Mechanical quadrature methods(MQMs) for solving nonlinear boundary integral equations of Helmholtz equation, which possessed high accuracy order O (h3) and low computing complexities, were presented. Moreover, the mechanical quadrature methods were simple without computing any singular integration. A nonlinear system was constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system were proved based on asymptotical compact theory and Stepleman theorem. Using the h3-Richardson extrapolation algorithms (EAs), the accuracy order to O (h5) was improved. For solving the nonlinear system, Newton iteration was discussed extensively by Ostrowski fixed point theorem. The efficiency of the algorithms was illustrated by numerical examples.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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