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Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
- Source :
- Mathematical Problems in Engineering, Vol 2018 (2018)
- Publication Year :
- 2018
- Publisher :
- Hindawi Limited, 2018.
-
Abstract
- 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.
- Subjects :
- Article Subject
lcsh:Mathematics
General Mathematics
General Engineering
Extrapolation
Richardson extrapolation
010103 numerical & computational mathematics
lcsh:QA1-939
01 natural sciences
Integral equation
Quadrature (mathematics)
010101 applied mathematics
Nonlinear system
Singularity
lcsh:TA1-2040
Applied mathematics
0101 mathematics
lcsh:Engineering (General). Civil engineering (General)
Asymptotic expansion
Compact convergence
Mathematics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2018
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....f973e51b0e253707b8880d27c4cec3a1