Numerical simulation of a class of integro-partial differential equations using a transformation technique (Q1372906)

The author describes a method for the numerical solution of a class of integro-partial differential equations (IPDEs), with integration being over \([0,\infty)\). The approach is based on transformation techniques (employing Laguerre polynomial expansions) which reduce the given system to an infinite system of ordinary differential equations. This class of IPDEs arises in ``mean-field'' models where the local behavior of an isolated element of the physical system depends on the local variable and on the mean of the system-averaged variables. The convergence of the method and its practical implementation are discussed in some detail.