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A comparison of Galerkin, collocation and the method of lines for partial differential equations
Author(s) -
Hopkins T. R.,
Wait R.
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620120703
Subject(s) - collocation method , mathematics , orthogonal collocation , galerkin method , discretization , ordinary differential equation , partial differential equation , collocation (remote sensing) , numerical partial differential equations , method of lines , mathematical analysis , exponential integrator , finite element method , differential equation , first order partial differential equation , stochastic partial differential equation , differential algebraic equation , computer science , physics , machine learning , thermodynamics
A number of numerical methods for parabolic paritial differential equations are discussed, they all reduce a single partial differential equation to a system of ordinary differential equations by discretization in the space variable(s). The discretizations can be finite element approximations (Galerkin and collocation) or finite difference approximations (methods of lines). The performances of the different methods are compared when used in conjunction with a variable time‐step ordinary differential equation integrator. Tables of results are given and the suitability of the discretizations is discussecd.