THE SOLVING LINEAR ONE-DIMEMSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND IN REPRODUCING KERNEL SPACE

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FAZLI A.; JAVADI SH.

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ISSN: 2588-4824

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:3 | Issue:12 Page(s): 79-86

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Title

THE SOLVING LINEAR ONE-DIMEMSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND IN REPRODUCING KERNEL SPACE

Author(s)

FAZLI A. | JAVADI SH. | Issue Writer Certificate

Keywords

VOLTERRA INTEGRAL EQUATIONQ1

REPRODUCING KERNELQ1

FOURIER COEFFICIENTSQ1

Abstract

In this paper, to solve a linear one-dimensional VOLTERRA INTEGRAL EQUATION of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and REPRODUCING KERNEL functions, we obtain a basis for the functions space. Then we obtain the solution of integral equation in terms of the basis functions. The examples presented in this paper show validity of the method. But this method does not provide results for nonlinear onedimensional VOLTERRA INTEGRAL EQUATIONs of the second kind. In this case for calculation Fourier cofficients the new method should be given. Thus the next focus on providing a method for calculating Fourier cofficients in the nonlinear mode. Also we think that this method can be generalized to linear two-dimensional VOLTERRA INTEGRAL EQUATIONs of the second kind and we worked on this in the another paper.

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APA: Copy

FAZLI, A., & JAVADI, SH.. (2018). THE SOLVING LINEAR ONE-DIMEMSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND IN REPRODUCING KERNEL SPACE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(12 ), 79-86. SID. https://sid.ir/paper/257372/en

Vancouver: Copy

FAZLI A., JAVADI SH.. THE SOLVING LINEAR ONE-DIMEMSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND IN REPRODUCING KERNEL SPACE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;3(12 ):79-86. Available from: https://sid.ir/paper/257372/en

IEEE: Copy

A. FAZLI, and SH. JAVADI, “THE SOLVING LINEAR ONE-DIMEMSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND IN REPRODUCING KERNEL SPACE,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 12 , pp. 79–86, 2018, [Online]. Available: https://sid.ir/paper/257372/en

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