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What Is the Numerical Method of Lines? Some Applications of the Numerical Method of Lines. Spatial Differentiation. Initial Value Integration. Stability of Numerical Method of Lines Approximations. Additional Applications: Multidimensional Pdes and Adaptive Grids. Appendix A: The Laplacian Operator in Various Coordinate Systems. Appendix B: Spatial Differentiation Routines. Appendix C: Library of ODE and ODE/PDE Applications. Index.
Hindmarsh et al. (Fri,) studied this question.