Three-step Method of Volterra Integral Equation of the Second Kind
D. Raymond
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
A. Adu *
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
P. O. Olanrewaju
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
R. Ajia
Department of Mathematics and Statistics, College of Agriculture, Science and Technology Jalingo, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The interpolation and collocation method has been used in this study to build a class of three step implicit second order derivative hybrid block methods for the solutions of the second kind of Volterra integral problems. After the continuous block techniques were evaluated at each step point, the discrete block methods could be reconstructed. Each discrete scheme obtained from the simultaneous solution of the block using the block methods confirmed that it had the same level of accuracy as the main endless approach. The new family of k-step procedures provides a high order of accuracy with exceedingly low error constants and stable intervals of absolute stability. The characteristics of the approaches revealed that they were convergent, zero-stable, and consistent. Results from two Volterra integral equations of the second kind showed that the new methods in the study achieved better than those we compared with in the literature.
Keywords: Volterra integral, trigonometric, hybrid point, off-grid, power series