Derivation of Continuous Linear Multistep Hybrid Block Method for the Solution of Volterra Integral Equation of Second Kind
John Chuseh Ahmadu
Department of Mathematics, University of Abuja, Nigeria.
F.O. Ogunfiditimi *
Department of Mathematics, University of Abuja, Nigeria.
I. Sale
Department of Mathematics, University of Abuja, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we proposed a continuous linear multistep hybrid block method for the solution of Volterra integral equation of second kind of the form y(x) = f (x) + \(f^{xn}_{xo}\) \(\varphi\)(x, s)y(s))ds, using power series and trigonometrically fitted function as the trial solution for the approximation via collocation techniques. The proposed hybrid block scheme is found to be consistent, zero-stable and convergent. The implementation of the scheme on numerical problems and comparisons of results obtained with existing numerical method will be included.
Keywords: Multistep hybrid block method, power series, collocation and interpolation method, second kind of Volterra integral equations