High-accuracy quadrature methods for solving nonlinear boundary integral equations of axisymmetric Laplace’s equation

2018 ◽  
Vol 37 (5) ◽  
pp. 6838-6847 ◽  
Author(s):  
Hu Li ◽  
Jin Huang
Keyword(s):  
Integral Equations ◽  
Nonlinear Boundary ◽  
Boundary Integral Equations ◽  
High Accuracy ◽  
Boundary Integral ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Quadrature Methods

scholarly journals Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Pan Cheng ◽  
Ling Zhang
Keyword(s):  
Asymptotic Expansion ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Boundary Integral Equations ◽  
Logarithmic Singularity ◽  
Nonlinear Problems ◽  
Boundary Integral ◽  
Convergence Theory ◽  
Mechanical Quadrature ◽  
Quadrature Methods

This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example.

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