A NUMERICAL APPROACH FOR SOLVING OF TWO- DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS WITH BOUBAKER POLYNOMIAL BASES

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MEHDIFAR F.; KHANI A.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:3 | Issue:12 Page(s): 41-54

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Title

A NUMERICAL APPROACH FOR SOLVING OF TWO- DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS WITH BOUBAKER POLYNOMIAL BASES

Author(s)

MEHDIFAR F. | KHANI A. | Issue Writer Certificate

Keywords

TWO-DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONSQ1

FUNDAMENTAL MATRIXQ1

TRUNCATED BOUBAKER POLYNOMIALS SERIESQ1

COLLOCATION METHODQ1

Abstract

In this paper, a new COLLOCATION METHOD, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of TWO-DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS of the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral equation to the solution of a system of algebraic equations. The precision and error analysis have been carefully and structurally studied and it has been emphasized that the proposed method for a variety of linear two-dimensional linear Fredholm linear integral equations with continuous kernel of polynomial type is completely accurate and error-free. On the other hand, with the help of the Maple Math Software, it is very easy to calculate the Boubaker polynomial coefficients of the solution. Also, we compared the results of present method with the results of other available methods to provide the validity, accuracy and efficiency of the technique.

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APA: Copy

MEHDIFAR, F., & KHANI, A.. (2018). A NUMERICAL APPROACH FOR SOLVING OF TWO- DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS WITH BOUBAKER POLYNOMIAL BASES. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(12 ), 41-54. SID. https://sid.ir/paper/257371/en

Vancouver: Copy

MEHDIFAR F., KHANI A.. A NUMERICAL APPROACH FOR SOLVING OF TWO- DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS WITH BOUBAKER POLYNOMIAL BASES. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;3(12 ):41-54. Available from: https://sid.ir/paper/257371/en

IEEE: Copy

F. MEHDIFAR, and A. KHANI, “A NUMERICAL APPROACH FOR SOLVING OF TWO- DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS WITH BOUBAKER POLYNOMIAL BASES,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 12 , pp. 41–54, 2018, [Online]. Available: https://sid.ir/paper/257371/en

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