A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations
In this paper, a novel meshless technique termed the random integral quadrature (RIQ) method is developed for the numerical solution of the second kind of the Volterra integral equations. The RIQ method is based on the generalized integral quadrature (GIQ) technique, and associated with the Kriging...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/106490 http://hdl.handle.net/10220/17986 http://dx.doi.org/10.1016/j.cam.2012.06.041 |
| _version_ | 1811680760326782976 |
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| author | Li, Hua. Zou, Hua. |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Li, Hua. Zou, Hua. |
| author_sort | Li, Hua. |
| collection | NTU |
| description | In this paper, a novel meshless technique termed the random integral quadrature (RIQ) method is developed for the numerical solution of the second kind of the Volterra integral equations. The RIQ method is based on the generalized integral quadrature (GIQ) technique, and associated with the Kriging interpolation function, such that it is regarded as an extension of the GIQ technique. In the GIQ method, the regular computational domain is required, in which the field nodes are scattered along straight lines. In the RIQ method however, the field nodes can be distributed either uniformly or randomly. This is achieved by discretizing the governing integral equation with the GIQ method over a set of virtual nodes that lies along straight lines, and then interpolating the function values at the virtual nodes over all the field nodes which are scattered either randomly or uniformly. In such a way, the governing integral equation is converted approximately into a system of linear algebraic equations, which can be easily solved. |
| first_indexed | 2024-10-01T03:30:10Z |
| format | Journal Article |
| id | ntu-10356/106490 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:30:10Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/1064902019-12-06T22:12:52Z A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations Li, Hua. Zou, Hua. School of Mechanical and Aerospace Engineering DRNTU::Engineering::Mechanical engineering In this paper, a novel meshless technique termed the random integral quadrature (RIQ) method is developed for the numerical solution of the second kind of the Volterra integral equations. The RIQ method is based on the generalized integral quadrature (GIQ) technique, and associated with the Kriging interpolation function, such that it is regarded as an extension of the GIQ technique. In the GIQ method, the regular computational domain is required, in which the field nodes are scattered along straight lines. In the RIQ method however, the field nodes can be distributed either uniformly or randomly. This is achieved by discretizing the governing integral equation with the GIQ method over a set of virtual nodes that lies along straight lines, and then interpolating the function values at the virtual nodes over all the field nodes which are scattered either randomly or uniformly. In such a way, the governing integral equation is converted approximately into a system of linear algebraic equations, which can be easily solved. 2013-12-02T08:29:40Z 2019-12-06T22:12:52Z 2013-12-02T08:29:40Z 2019-12-06T22:12:52Z 2013 2013 Journal Article Li, H., & Zou, H. (2013). A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations. Journal of computational and applied mathematics, 237(1), 35-42. 0377-0427 https://hdl.handle.net/10356/106490 http://hdl.handle.net/10220/17986 http://dx.doi.org/10.1016/j.cam.2012.06.041 en Journal of computational and applied mathematics |
| spellingShingle | DRNTU::Engineering::Mechanical engineering Li, Hua. Zou, Hua. A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations |
| title | A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations |
| title_full | A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations |
| title_fullStr | A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations |
| title_full_unstemmed | A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations |
| title_short | A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations |
| title_sort | random integral quadrature method for numerical analysis of the second kind of volterra integral equations |
| topic | DRNTU::Engineering::Mechanical engineering |
| url | https://hdl.handle.net/10356/106490 http://hdl.handle.net/10220/17986 http://dx.doi.org/10.1016/j.cam.2012.06.041 |
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