Abstract
In this work, a mechanical quadrature method based on modified trapezoid formula is used for solving weakly singular Volterra integral equation with proportional delays. An improved Gronwall inequality is testified and adopted to prove the existence and uniqueness of the solution of the original equation. Then, we study the convergence and the error estimation of the mechanical quadrature method. Moreover, Richardson extrapolation based on the asymptotic expansion of error not only possesses a high accuracy but also has the posterior error estimate which can be used to design self-adaptive algorithm. Numerical experiments demonstrate the efficiency and applicability of the proposed method.
Highlights
In recent years, Volterra integral equation with delay has received a considerable amount of attention
This paper considers the following weakly singular Volterra integral equations with proportional delays: u (t) = g (t) + (Iu) (t) + (Iθu) (t), t ∈ I = [0, T], (1)
Delay integral equation and partial differential equation have been widely used in many population growth and relevant phenomena in mathematical biology [1,2,3]
Summary
Volterra integral equation with delay has received a considerable amount of attention. This paper considers the following weakly singular Volterra integral equations with proportional delays:. Vast researchers focused their interests on the numerical techniques of delay integral equations with continuous kernels, such as least squares approximation method [12], spectral method [13], Bernoulli wavelet method [14], and collocation method [15]. The equation is approximated by employing the floor technique to the delay argument θ(t) and by adopting the quadrature formula [20] to the weakly integrals.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
