NONLINEAR MODELS AND PROBLEMS IN APPLIED SCIENCES FROM DIFFERENTIAL QUADRATURE TO GENERALIZED COLLOCATION METHODS

This paper deals with the developments of mathematical methods for the discretization of continuous models and the solution of nonlinear pro blems of interest in applied sciences. In particular, the contents ref er to developments of the differential quadrature method proposed by B ellmann, Kashef and Casti, which leads to the so called generalized co llocation methods. The contents is in three parts. The first one is a general description of the method for the solution of initial-boundary value problems. The second part is on recent developments of the meth od both towards the solution of different classes of problems, e.g., s olution of integro-differential equations, domain decomposition and st ochastic problems. The third part is on improvements of solution algor ithms, on computation of error estimates, and research perspectives. T he whole content is constantly referred to the solution of nonlinear p roblems in applied sciences.