THEORY OF BLOCK-PULSE FUNCTIONS IN NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

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ABDOLLAHI A.; BABOLIAN E.

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Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2016 | Volume:8 | Issue:2 Page(s): 157-163

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Title

THEORY OF BLOCK-PULSE FUNCTIONS IN NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

Author(s)

ABDOLLAHI A. | BABOLIAN E. | Issue Writer Certificate

Keywords

BLOCK-PULSE FUNCTIONSQ2

FREDHOLM INTEGRAL EQUATIONQ2

LEAST SQUARES APPROXIMATIONQ2

Abstract

Recently, the BLOCK-PULSE FUNCTIONS (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear FREDHOLM INTEGRAL EQUATIONs (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a main part. By providing a new method based on BPFs for solving FIEs of the second kind, the least squares and non-least squares solutions are defined for this problem. First, the convergence of the non-least squares solution is proved by the Nystrom method. Then, considering the fact that the set of all invertible matrices is an open set, the convergence of the least squares solution is investigated. The convergence of Nystrom method has the main role in proving the basic results. Because the presented convergence trend is independent of the orthogonality of the basis functions, the given method can be applied for any arbitrary method.

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APA: Copy

ABDOLLAHI, A., & BABOLIAN, E.. (2016). THEORY OF BLOCK-PULSE FUNCTIONS IN NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 8(2), 157-163. SID. https://sid.ir/paper/231711/en

Vancouver: Copy

ABDOLLAHI A., BABOLIAN E.. THEORY OF BLOCK-PULSE FUNCTIONS IN NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2016;8(2):157-163. Available from: https://sid.ir/paper/231711/en

IEEE: Copy

A. ABDOLLAHI, and E. BABOLIAN, “THEORY OF BLOCK-PULSE FUNCTIONS IN NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 8, no. 2, pp. 157–163, 2016, [Online]. Available: https://sid.ir/paper/231711/en

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