Solution of Some Integral Equations by Point-Collocation Method

Authors : Birkan Durak, Hasan Ömür Özer, Şule Kapkin, Hüseyin Yildiz

Pages : 1894-1905

Doi:10.31466/kfbd.1372548

View : 91 | Download : 56

Publication Date : 2023-12-15

Article Type : Research Paper

Abstract :In several engineering or physics problems, particularly those involving electromagnetic theory, thermal and radiation effects, acoustics, elasticity, and some fluid mechanics, it is not always easy or possible to find the analytical solution of integral equations that describe them. For this reason, numerical techniques are used. In this study, Point-collocation method was applied to linear and nonlinear, Volterra and Fredholm type integral equations and the performance and accuracy of the method was compared with several other methods that seem to be popular choices. As the base functions, a suitably chosen family of polynomials were employed. The convergence of the method was verified by increasing the number of polynomial base functions. The results demonstrate that the collocation method performs well even with a relatively low number of base functions and is a good candidate for solving a wide variety of integral equations. Nonlinear problems take longer to calculate approximate solution coefficients than linear problems. Furthermore, it is necessary to use the real and smallest coefficients found in order to obtain a suitable approximate solution to these problems.
Keywords : Kollokasyon yöntemi, Doğrusal olmayan integral denklemler, Volterra denklemleri, Fredholm denklemleri, Yaklaşık çözüm yöntemi