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Method of Lines MOL and Differential Algebraic Equations DAE

Wu and White [577] have described a new method that is reminiscent of the earher work of Kimble and White [338] but makes use of the Hermitian method (that is, using derivatives) to achieve higher-order solutions for several concentration rows at a time. They also suggest, but do not demonstrate, the use of their new scheme as a possible start-up for BDF. The reader is referred to their paper for details. [Pg.165]

The Method of Lines or MOL is not so much a particular method as a way of approaching numerical solutions of pdes. It is described well by Hartree [295] as the replacement of the second-order (space) derivative by a finite difference that is, leaving the first (time) derivative as it is, thus forming from, say, the diffusion equation a set of ordinary differential equations, to be solved in an unspecified manner. Thus, a system such as (9.17) on page 151, can be written in the general vector-matrix form [Pg.165]

The method has a long history. The name MOL seems to have become estabhshed around 1960. Before this, various authors either used the word line [254] or expressions like on certain lines [330] or a description of the idea. In the book by Kantorovich and Krylov [330], there is a reference to a 1934 paper [329]. It is also cited by Liskovets [366] as a source paper, along with Rothe (1930) [475], who might be the first. Hartree and Womersley [296] use, in their summary, the words approximating by use of finite intervals in one variable, and integrating exactly in the other variable . The book by Schiesser [497] is the standard work now (he calls the method NUMOL, for numerical method of hnes). Electrochemical use of MOL has been sparse. Lemos and coworkers [357, 359, 360] have investigated the method, using [Pg.165]


Method of Lines (MOL) and Differential Algebraic Equations (DAE) 165 Method of Wu and White... [Pg.165]




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Algebra methods)

Algebraic method

Differential algebraic equations

Differential algebraic equations (DAEs)

Differential and algebraic equations

Differential equations method

Differential method

Equation of line

Equations algebraic

Line methods

Method of lines

Mol

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