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The method of lines, where all but one variable is discretized.
It is also possible to solve elliptical problems by a semi-analytical method of lines (Subramanian, 2004).
The method of lines in this context dates back to at least the early 1960s Sarmin and Chudov.
Semianalytical method of lines for solving elliptic partial differential equations, Chemical Engineering Science, 59, 781-788.
The Method Of Lines (MOL)
W. E. Schiesser of Lehigh University is one of the major proponents of the method of lines, having published widely in this field.
If we integrate the hyperbolic problem over a control volume we obtain a Method of lines (MOL) formulation for the spatial cell averages:
Many papers discussing the accuracy and stability of the method of lines for various types of partial differential equations have appeared since (for example Zafarullah or Verwer and Sanz-Serna).
P. W. C. Northrop, P. A. Ramachandran, W. E. Schiesser, and V. R. Subramanian, "A Robust False Transient Method of Lines for Elliptic Partial Differential Equations," Chem.
Wörterbuch für Mathematik