The Numerical Method of Lines for Partial Differential ...

1 The Numerical Method of Lines for PartialDifferential Equationsby Michael B. Cutlip, University of Connecticut andMordechai Shacham, Ben-Gurion University of the NegevThe Method of Lines is a general technique for solving Partial Differential equations (PDEs) by typically using finite difference relationships for the spatial derivatives andordinary Differential equations for the time derivative. William E. Schiesser at LehighUniversity has been a major proponent of the Numerical Method of Lines , Thissolution approach can be very useful with undergraduates when this technique isimplemented in conjunction with a convenient ODE solver package such Problem in Unsteady-State Heat Transfer3 This approach can be illustrated by considering a problem in unsteady-state heatconduction in a one-dimensional slab with one face insulated and constant thermalconductivity as discussed by heat transfer in a slab in the x direction is described by the partialdifferential equation22xTtT = (1)where T is the temperature in K, t is the time in s, and is the thermal diffusivity in m2/sgiven by k/ cp.

3 The problem then requires the solution of Equations (3), (5), and (7) which results in nine simultaneous ordinary differential equations and two explicit algebraic

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  Methods, Line, Differential, Equations, Differential equations, Method of lines

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