Volume 29, Issue 3
High Order Numerical Methods to Two Dimensional Heaviside Function Integrals

J. Comp. Math., 29 (2011), pp. 305-323.

Published online: 2011-06

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• Abstract

In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimensional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function integral is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the second- to fourth-order methods implemented in this paper achieve or exceed the expected accuracy.

• Keywords

Heaviside function integral, High order numerical method, Irregular domain

65D05, 65D30, 65D32.

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@Article{JCM-29-305, author = {}, title = {High Order Numerical Methods to Two Dimensional Heaviside Function Integrals}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {3}, pages = {305--323}, abstract = {

In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimensional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function integral is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the second- to fourth-order methods implemented in this paper achieve or exceed the expected accuracy.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1010-m3285}, url = {http://global-sci.org/intro/article_detail/jcm/8480.html} }
TY - JOUR T1 - High Order Numerical Methods to Two Dimensional Heaviside Function Integrals JO - Journal of Computational Mathematics VL - 3 SP - 305 EP - 323 PY - 2011 DA - 2011/06 SN - 29 DO - http://doi.org/10.4208/jcm.1010-m3285 UR - https://global-sci.org/intro/article_detail/jcm/8480.html KW - Heaviside function integral, High order numerical method, Irregular domain AB -

In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimensional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function integral is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the second- to fourth-order methods implemented in this paper achieve or exceed the expected accuracy.

Xin Wen. (1970). High Order Numerical Methods to Two Dimensional Heaviside Function Integrals. Journal of Computational Mathematics. 29 (3). 305-323. doi:10.4208/jcm.1010-m3285
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