A new eighth-order A-stable method for solving differential systems arising in chemical reactions

摘要

Implicit Runge-Kutta methods are successful algorithms for the numerical solution of stiff differential equations, as they usually appear in chemical reactions. This article describes the construction of a particular implicit method based on internal stages obtained from certain Chebyshev collocation points. The resulting method has algebraic order 8 and A-stability characteristic. An embedding technique using the Runge-Kutta method and a linear multistep one is provided in order to change the step size. Numerical experiments illustrate the behaviour of the new method, showing that it may reach great accuracy and be competitive with other well-known codes.