Three-Step Three off Grid Points for Solving Volterra Integral Equation of the Second Kind
Adu, A. *
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
Ine, Nyiutya Cephas
Our Lady of Mount Carmel College, Makurdi, Nigeria.
John., Chuseh Ahmadu
University of Abuja, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The second order Volterra linear integral problem of the second kind was expressed and solved by the hybrid block three-step approach of order six. The method was created with the use of interpolation and a collocation approach, utilizing power series and the trigonometric functions as the basis function. We investigate the method's properties, including order, consistency, and region of absolute stability. Next, the second kind problem's linear Volterra integral equation was resolved, and the numerical outcome demonstrated that the hybrid block technique's accuracy and efficiency outperformed Rouibah et al.'s (2022) method in terms of both accuracy and efficiency.
Keywords: Linear, volterra, second derivative, power series, trigonometric, hybrid point