in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

In this paper, a collocation method based on the Bernstein polynomials is presented for the fractional Riccati type differential equations. By writing t? ta (0 < a < 1) in the truncated Bernstein series, the truncated fractional Bernstein series is obtained and then it is transformed into the matrix form. By using Caputo fractional derivative, the matrix forms of the fractional derivatives are ...

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equat...

In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.    

this paper gives an ecient numerical method for solving the nonlinear systemof volterra-fredholm integral equations. a legendre-spectral method based onthe legendre integration gauss points and lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

The problems of radiative transfer give rise to interesting integral equations that must be faced with efficient numerical solver. Very often the integral equations are discretized to large-scale nonlinear equations and solved by Newton’s-like methods. Generally, these kind of methods require the computation and storage of the Jacobian matrix or its approximation. In this paper, we present a ne...

This paper introduces the Global-Local Mapping Approximation algorithm as a candidate for identifying nonlinear, six degree-of-freedom rigid body aircraft dynamics. The technique models the nonlinear dynamical model as a sum of linear model and nonlinear model. The linear model dynamics are assumed to be perturbed by a nonlinear term which represents the system nonlinearities that are not captu...

In this paper, we utilize the Riemann–Hilbert approach to discuss multi-soliton solutions of N-component nonlinear Schrödinger equations. Firstly, by transformed Lax pair, construct matrix-valued functions $$P_{1,2}$$ that satisfy analyticity and normalization corresponding jump matrix can be determined. Then, in reflectionless case, get $$q_{l}$$ $$(l=1,\ldots ,N)$$ equations, which are relate...

In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...

Nonlinear state-space models driven by differential equations have been widely used in science. Their statistical inference generally requires computing the mean and covariance matrix of some nonlinear function of the state variables, which can be done in several ways. For example, such computations may be approximately done by Monte Carlo, which is rather computationally expensive. Linear appr...