An exponential method to solve linear Fredholm-Volterra  integro-differential equations and residual improvement

Şuayip YÜZBAŞI

Makale detayları

An exponential method to solve linear Fredholm-Volterra integro-differential equations and residual improvement

Yazarlar:

Şuayip YÜZBAŞI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2546-2562

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745780

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this paper, a collocation approach based on exponential polynomials is introduced to solve linear Fredholm-Volterra integro-differential equations under the initial boundary conditions. First, by constructing the matrix forms of the exponential polynomials and their derivatives, the desired exponential solution and its derivatives are written in matrix forms. Second, the differential and integral parts of the problem are converted into matrix forms based on exponential polynomials. Later, the main problem is reduced to a system of linear algebraic equations by aid of the collocation points, the matrix operations, and the matrix forms of the conditions. The solutions of this system give the coefficients of the desired exponential solution. An error estimation method is also presented by using the residual function and the exponential solutions are improved by the estimated error function. Numerical examples are solved to show the applicability and the effectiveness of the method. In addition, the results are compared with the results of other methods.

Makale detayları

An exponential method to solve linear Fredholm-Volterra integro-differential equations and residual improvement

Yazarlar: Şuayip YÜZBAŞI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2546-2562

Belge Tipi: Makale

Yayın Tarihi: 9/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745780

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Şuayip YÜZBAŞI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2546-2562

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745780

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098