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ODE solvers and the method of lines
Author(s) -
Shampine L. F.
Publication year - 1994
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.1690100608
Subject(s) - ode , solver , mathematics , method of lines , nonlinear system , advection , calculus (dental) , mathematical analysis , mathematical optimization , differential equation , ordinary differential equation , physics , differential algebraic equation , quantum mechanics , thermodynamics , medicine , dentistry
Factors influencing the choice of ODE solver for the numerical solution of PDEs by the method of lines are investigated. The advection—diffusion equation is used to gain insight that is generalized to some classes of nonlinear PDEs. Numerical results for several nonlinear PDEs illustrate the theoretical developments. © 1994 John Wiley & Sons, Inc.