Akademik Veri Yönetim Sistemi
Karadeniz Fen Bilimleri Dergisi, cilt.13, sa.4, ss.1894-1905, 2023 (TRDizin)
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.