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The Multi‐Grid Method in the Solution of Time‐Dependent Nonlinear Partial Differential Equations
Author(s) -
De Vries H. B.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860661106
Subject(s) - numerical partial differential equations , nonlinear system , exponential integrator , mathematics , partial differential equation , method of characteristics , numerical methods for ordinary differential equations , multigrid method , method of lines , mathematical analysis , ordinary differential equation , first order partial differential equation , stochastic partial differential equation , differential equation , separable partial differential equation , collocation method , differential algebraic equation , physics , quantum mechanics
The numerical solution of nonlinear, time‐dependent partial differential equations is discussed. By applying the method of lines such a partial differential equation is converted into a system of ordinary differential equations to which an implicit linear multistep method is applied. Using Newton iteration the nonlinear implicit relations are replaced by a sequence of linear equations. These linear equations are solved by the iterative use of a multi‐level algorithm. Numerical examples are given and a comparison is made with other integration techniques.