an:01135913
Zbl 0898.65074
Bellomo, N.
Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods
EN
Math. Comput. Modelling 26, No. 4, 13-34 (1997).
00044142
1997
j
65N35 65R20 45K05 60H15 65N15 65N55 35J65 65C99
differential quadrature method; nonlinear problems; collocation method; integro-differential equations; domain decomposition; stochastic problems; algorithms; error estimates
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.
W.Heinrichs (Essen)
Zbl 0247.65061