in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

We study a family of unbounded solutions to the Korteweg–de Vries equation which can be constructed as log-derivatives deformed Airy kernel Fredholm determinants, and are connected an integro-differential version second Painlevé equation. The initial data well-defined for $$x>0$$ , but not $$x<0$$ where behave like $$\frac{x}{2t}$$ $$t\rightarrow 0$$ hence would cylindrical provide uniform asym...

The aim of this paper is to carry out an improved analysis the convergence Nyström and degenerate kernel methods their superconvergent versions for numerical solution a class linear Fredholm integro-differential equations second kind. By using interpolatory projection at Gauss points onto space (discontinuous) piecewise polynomial functions degree ?r?1, we obtain order 2r methods, while, iterat...

In this paper, two collocation methods based on the shifted Legendre polynomials are proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations. The equation considered in paper involves derivative unknown functions integral term, which makes its numerical solution more complicated. We first introduce a single-step method interval [0, 1]. Next, multi-step version ...