Stiff ode slovers: a review of current and coming attractions
Journal of Computational Physics
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Software for Nonlinear Partial Differential Equations
ACM Transactions on Mathematical Software (TOMS)
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The original amplitude-shape method [N. Parumasur, Amplitude-Shape Method for the Numerical Solution of Ordinary Differential Equations, Ph.D. Thesis, Department of Mathematics, University of Natal, Durban, 1997; Quaestiones Math. 24 (2001) 69] for solving ordinary differential equations consisted in transforming certain systems of stiff ordinary differential equations into two subsystems consisting of a rapidly changing amplitude function and slowly varying shape vector, respectively. In this paper we consider a new formulation of the amplitude and shape equations, which is particularly well suited for certain classes of problems occurring in chemical kinetics. The resulting equations are treated with a partitioned method consisting of the Rosenbrock method and the trapezoidal rule. It is shown that the use of the proposed new version of the amplitude-shape method leads to a substantial gain in computational efficiency in comparison with the conventional implicit or semi-implicit schemes employed in stiff solvers.