The further study of a certain nonlinear integro-differential equation (Q1093353)

The authors obtain a global existence and uniqueness theorem for a nonlinear Volterra integro-differential equation which occurs in the statistical theory of turbulent diffusion. They employ implicit Runge- Kutta methods with m stages and optimal order \(p=2m\) to obtain an approximate solution of the equation. Some numerical examples are considered to demonstrate the advantage of their techniques over others.