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 work we consider a certain class of Volterra integral equations possessing an infinite set of solutions. We investigate the application of Euler’s method together with the use of extrapolation procedures. Several examples are considered illustrating our results as well as the use of graded meshes and the application of higher order methods. keywords Volterra integral equations; weakly s...

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.

In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions ...

In this paper, the solution of a moving Volterra-type screw dislocation in an orthotropic layer, bonded between two piezoelectric layers is obtained using complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple moving cracks. These equations, which are classified as, Cauchy singular equations, ...

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...