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Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems
Author(s) -
Ramachandran P.A.
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20121
Subject(s) - mathematics , discretization , linearization , representation (politics) , partial differential equation , nonlinear system , boundary element method , boundary (topology) , mathematical analysis , method of lines , boundary value problem , variable (mathematics) , finite element method , differential equation , ordinary differential equation , differential algebraic equation , physics , quantum mechanics , politics , political science , law , thermodynamics
Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006