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Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods. (English) Zbl 0898.65074
Mathematical methods for nonlinear problems in applied sciences are investigated. The contents are based on a quadrature method proposed by R. Bellmann, B. G. Kashef and 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.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65N15 Error bounds for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65C99 Probabilistic methods, stochastic differential equations
Full Text: DOI
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