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...