In this paper, based on the modified block-by-block method, we propose a higher-order numerical scheme for two-dimensional nonlinear fractional Volterra integral equations with uniform accuracy. This approach involves discretizing domain into large number of subdomains and using biquadratic Lagrangian interpolation each subdomain. The convergence high-order is rigorously established. We prove t...

in this paper, we present a numerical method for solving nonlinear fredholm and volterra integral equations of the second kind which is based on the use of haar wavelets and collocation method. we use properties of block pulse functions (bpf) for solving volterra integral equation. numerical examples show efficiency of the method.

Abstract The functional equations, functional integral equations and functional differential equations have many applications in nonlinear analysis. Also, the fractional order integral equations and fractional order differential equations have many applications in mathematical physics. Here we study the existence of solutions of a functional integral equations of arbitrary (fractional) order in...

asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.we have used a general method, based on zakharov integral equation.on the basis of these evolution eq...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

This paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra integral equations system. To showthe advantages of our method some numerical examples are presented.