Some Extended Explicit Bel'tyukov Pairs for Volterra Integral Equations of the Second Kind
SIAM Journal on Numerical Analysis
On approximate solution of Hammerstein integral equations in the space Lp (p ≥ 1)
Applied Mathematics and Computation
Double exponential formulas for numerical indefinite integration
Journal of Computational and Applied Mathematics
Monotonic solutions of a class of quadratic integral equations of Volterra type
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Computational Mathematics and Mathematical Physics
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We consider a paper of Banas and Sadarangani (2008) [11] which deals with monotonicity properties of the superposition operator and their applications. An application of the monotonicity properties is to study the solvability of a quadratic Volterra integral equation. In this paper, we prepare an efficient numerical technique based on the fixed point method and quadrature rules to approximate a solution for quadratic Volterra integral equation. Then convergence of numerical scheme is proved by some theorems and some numerical examples are given to show applicability and accuracy of the numerical method and guarantee the theoretical results.