Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods (Q1381784)

Mathematical methods for nonlinear problems in applied sciences are investigated. The contents are based on a quadrature method proposed by \textit{R. Bellmann, B. G. Kashef} and \textit{J. Casti} [J. Comput. Phys. 10, 40-52 (1972; Zbl 0247.65061)], which leads to the so called generalized collocation method. First, a general description is given. Then recent developments concerning integro-differential equations, domain decomposition and stochastic problems are discussed. Finally, improvements in the algorithms and computation of error estimates are given.