The rate of convergence of an iterative‐computational algorithm for second‐kind nonlinear Volterra integral equations with weakly singular kernels.

This paper attempts to present an iterative‐computational method for solving weakly singular nonlinear Volterra integral equations (WSNVIEs) of the second type based on rationalized Haar wavelets (RHWs). The proposed algorithm does not need to solve any linear or nonlinear system for evaluating the wavelet coefficients. After a brief introduction of rationalized Haar functions (RHFs), the computational matrices of integration and fractional integral are applied to reduce the approximation of integral equations to some matrix algebraic equations. Next, the error analysis of the problem by using the two‐dimensional iterated projection operator is offered. We will prove that the rate of convergence of the proposed algorithm is O(βh), where h is the iteration number and β is the contraction constance. The method for any WSNVIE of the second kind with 0 ≤ β < 1 is convergent. The proposed method is computationally attractive, and comparing the results obtained of the known technique is more efficient. [ABSTRACT FROM AUTHOR]