This paper concerns the integral equation

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

in this paper, a numerical efficient method based on two-dimensional block-pulse functions (bpfs) is proposed to approximate a solution of the two-dimensional linear stochastic volterra-fredholm integral equation. finally the accuracy of this method will be shown by an example.

This paper presents a numerical method for solving the Volterra integral equation with a convolution kernel. The integral equation was first converted to an algebraic equation using the Laplace transform, after which its numerical inversion was determined by power series. The Padé approximants were effectively used to improve the convergence rate and accuracy of the computed series. The method ...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...

Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together with their geometric interpretation: (i) the discrete coupled Volterra system for the coefficients of the Laplace equation, (ii) the gauge invariant form of the Hirota equation for projective invari...

The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation actually completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifu...

In this article, by means of using discrete zero curvature representation and constructing opportune time evolution problems, two new discrete integrable lattice hierarchies with ndependent coefficients are proposed, which related to a new discrete Schrödinger nonisospectral operator equation. The relation of the two new lattice hierarchies with the Volterra hierarchy is discussed. It has been ...