New NAG library software for first-order partial differential equations

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Abstract
New NAG Fortran Library routines are described for the solution of systems of nonlinear, first-order, time-dependent partial differential equations in one space dimension, with scope for coupled ordinary differential or algebraic equations. The method-of-lines is used with spatial discretization by either the central-difference Keller box scheme or an upwind scheme for hyperbolic systems of conservation laws. The new routines have the same structure as existing library routines for the solution of second-order partial differential equations, and much of the existing library software is reused. Results are presented for several computational examples to show that the software provides physically realistic numerical solutions to a challenging class of problems.