A C1 interpolant for codes based on backward differentiation formulae
Applied Numerical Mathematics
Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations
Applied Numerical Mathematics - Special issue on numerical methods for the Euler equation
Construction of explicit and implicit symmetric tvd schemes and their applications
Journal of Computational Physics
Courant-like conditions limit reasonable mesh refinement to order h2
SIAM Journal on Scientific and Statistical Computing
Applied Numerical Mathematics
Designing software for one-dimensional partial differential equations
ACM Transactions on Mathematical Software (TOMS)
A method for the spatial discretization of parabolic equations in one space variable
SIAM Journal on Scientific and Statistical Computing
A study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Developments in the NAG library software at IMSL
Scientific software systems
An adaptive theta method for the solution of stiff and nonstiff differential equations
Applied Numerical Mathematics
A Survey of Software for Partial Differential Equations
ACM Transactions on Mathematical Software (TOMS)
SPRINT2D: adaptive software for PDEs
ACM Transactions on Mathematical Software (TOMS)
A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Parallel implementation of a computational model of the human immune system
Euro-Par 2010 Proceedings of the 2010 conference on Parallel processing
Oscillatory combustion in closed vessels under microgravity
Mathematical and Computer Modelling: An International Journal
A three-dimensional computational model of the innate immune system
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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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.