Volume 10, Issue 5
The LMAPS Using Polynomial Basis Functions for Near-Singular Problems

Zhengzhi Li, Daniel Watson, Ming Li & Thir Dangal

Adv. Appl. Math. Mech., 10 (2018), pp. 1090-1102.

Published online: 2018-07

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  • Abstract

In this paper, we combine the Local Method of Approximate Particular Solutions (LMAPS) with polynomial basis functions to solve near-singular problems. Due to the unique feature of the local approach, the LMAPS is capable of capturing the rapid variation of the solution. Polynomial basis functions can become very unstable when the order of the polynomial becomes large. However, since the LMAPS is a local method, the order does not need to be very high; an order of 5 can achieve sufficient accuracy. In order to show the effectiveness of the LMAPS using polynomial basis functions for solving near singular problems, we compare the results to the LMAPS using radial basis functions (RBFs). The advantage of using polynomials as a basis rather than RBFs is that finding an appropriate shape parameter is not necessary.

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@Article{AAMM-10-1090, author = {}, title = {The LMAPS Using Polynomial Basis Functions for Near-Singular Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {5}, pages = {1090--1102}, abstract = {

In this paper, we combine the Local Method of Approximate Particular Solutions (LMAPS) with polynomial basis functions to solve near-singular problems. Due to the unique feature of the local approach, the LMAPS is capable of capturing the rapid variation of the solution. Polynomial basis functions can become very unstable when the order of the polynomial becomes large. However, since the LMAPS is a local method, the order does not need to be very high; an order of 5 can achieve sufficient accuracy. In order to show the effectiveness of the LMAPS using polynomial basis functions for solving near singular problems, we compare the results to the LMAPS using radial basis functions (RBFs). The advantage of using polynomials as a basis rather than RBFs is that finding an appropriate shape parameter is not necessary.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0288}, url = {http://global-sci.org/intro/article_detail/aamm/12590.html} }
TY - JOUR T1 - The LMAPS Using Polynomial Basis Functions for Near-Singular Problems JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1090 EP - 1102 PY - 2018 DA - 2018/07 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0288 UR - https://global-sci.org/intro/aamm/12590.html KW - AB -

In this paper, we combine the Local Method of Approximate Particular Solutions (LMAPS) with polynomial basis functions to solve near-singular problems. Due to the unique feature of the local approach, the LMAPS is capable of capturing the rapid variation of the solution. Polynomial basis functions can become very unstable when the order of the polynomial becomes large. However, since the LMAPS is a local method, the order does not need to be very high; an order of 5 can achieve sufficient accuracy. In order to show the effectiveness of the LMAPS using polynomial basis functions for solving near singular problems, we compare the results to the LMAPS using radial basis functions (RBFs). The advantage of using polynomials as a basis rather than RBFs is that finding an appropriate shape parameter is not necessary.

Zhengzhi Li, Daniel Watson, Ming Li & Thir Dangal. (1970). The LMAPS Using Polynomial Basis Functions for Near-Singular Problems. Advances in Applied Mathematics and Mechanics. 10 (5). 1090-1102. doi:10.4208/aamm.OA-2017-0288
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