The method of lines (MOL, NMOL, NUMOL[1][2][3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. By reducing a PDE to a single continuous dimension, the method of lines allows solutions to be computed via methods and software developed for the numerical integration of ordinary differential equations (ODEs) and differential-algebraic systems of equations (DAEs). Many integration routines have been developed over the years in many different programming languages, and some have been published as open source resources.[4]
The method of lines most often refers to the construction or analysis of numerical methods for partial differential equations that proceeds by first discretizing the spatial derivatives only and leaving the time variable continuous. This leads to a system of ordinary differential equations to which a numerical method for initial value ordinary equations can be applied. The method of lines in this context dates back to at least the early 1960s.[5] Many papers discussing the accuracy and stability of the method of lines for various types of partial differential equations have appeared since.[6][7]
^Schiesser, W. E. (1991). The Numerical Method of Lines. Academic Press. ISBN 0-12-624130-9.
^Hamdi, S.; W. E. Schiesser; G. W. Griffiths (2007), "Method of lines", Scholarpedia, 2 (7): 2859, Bibcode:2007SchpJ...2.2859H, doi:10.4249/scholarpedia.2859
^Schiesser, W. E.; G. W. Griffiths (2009). A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab. Cambridge University Press. ISBN 978-0-521-51986-1.
^Lee, H. J.; W. E. Schiesser (2004). Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple and Matlab. CRC Press. ISBN 1-58488-423-1.
^E. N. Sarmin; L. A. Chudov (1963), "On the stability of the numerical integration of systems of ordinary differential equations arising in the use of the straight line method", USSR Computational Mathematics and Mathematical Physics, 3 (6): 1537–1543, doi:10.1016/0041-5553(63)90256-8
^A. Zafarullah (1970), "Application of the Method of Lines to Parabolic Partial Differential Equations With Error Estimates", Journal of the Association for Computing Machinery, vol. 17, no. 2, pp. 294–302, doi:10.1145/321574.321583, S2CID 15114435
^J. G. Verwer; J. M. Sanz-Serna (1984), "Convergence of method of lines approximations to partial differential equations", Computing, 33 (3–4): 297–313, doi:10.1007/bf02242274, S2CID 30171258
system of ordinary differential equations to which a numerical method for initial value ordinary equations can be applied. The methodoflines in this...
secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can...
The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century...
information. The methodof loci is also known as the memory journey, memory palace, journey method, memory spaces, or mind palace technique. This method is a mnemonic...
The Nazca lines (/ˈnɑːzkə/, /-kɑː/) are a group of geoglyphs made in the soil of the Nazca Desert in southern Peru. They were created between 500 BC and...
States Air Force's crewed spaceflight program Methodof levels, a method in psychotherapy Methodoflines, a technique for solving partial differential...
of yin (broken) or yang (solid) lines, and commentaries on them. There are two main methodsof building up the linesof the hexagram, using either 50 yarrow...
Parallel Lines is the third studio album by American rock band Blondie, released on September 23, 1978, by Chrysalis Records to international commercial...
of suicide crisis lines and information about risk factors for suicide, and reporting on suicide as a multi-faceted, treatable health issue. Method restriction...
contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour...
Time in physics William Lax The Methodof Fluxions and Infinite Series: With Its Application to the Geometry of Curve-lines. By Sir Isaac Newton, Translated...
Ley lines (/leɪˈlaɪnz/) are straight alignments drawn between various historic structures, prehistoric sites and prominent landmarks. The idea was developed...
differential equations (ODEs) using the methodoflines to convert the partial derivatives on the right-hand side of the equation into appropriate finite...
This is a list of numerical analysis topics. Validated numerics Iterative method Rate of convergence — the speed at which a convergent sequence approaches...
Television lines (TVL) is a specification of an analog camera or monitor's horizontal image resolution. The TVL is one of the most important resolution...
regula falsi, methodof false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified...
'intercept'. The method yields a line of position (LOP) on which the observer is situated. The intersection of two or more such lines will define the observer's...
The Fraunhofer lines are a set of spectral absorption lines. They are dark absorption lines, seen in the optical spectrum of the Sun, and are formed when...
Asia INDO LINES, callsign of Indonesian Airlines Indo people, people of mixed European and Indonesian ancestry Indo cuisine, fusion cuisine of Indonesian...