Showing papers on "L-stability published in 1986"
TL;DR: In this paper, two finite-difference methods are proposed for solving wave instability problems with and without coupling between momentum and energy equations, and the results are compared with those generated by the Runge-Kutta integration method in conjunction with an orthonormalization procedure.
Abstract: Two finite-difference methods are proposed for solving wave instability problems with and without coupling between momentum and energy equations. Neutral critical stability results are compared with those generated by the Runge-Kutta integration method in conjunction with an orthonormalization procedure. The new finite-difference methods are found to be very accurate, timesaving, and easy to program. They can also be applied to solve systems of high-order ordinary differential equations.
26 citations
01 Jan 1986
TL;DR: In this article, the authors considered differential equations of the following type: ==================\/\/\/\/\/\/££€£££$££ £££•££'(t)'s = \,f(t,\,x(t)\,€£ £ £ ££,££(t),€£'££',££''(t'),££
Abstract: Many authors comp. [2], [5], [10], [11] considered differential equations of the following type:
$$x'(t)\, = \,f(t,\,x(t)\,,\,x'\,(t)).$$
(1)
where f: [0,a] x Rn x Rn → Rn is a continuous map satisfying some suitable assumptions.
6 citations
TL;DR: In this paper, a numerical method for the integration of chemical rate equations is presented, taking advantage of the fact that the Jacobian matrix is readily obtainable for this type of problem.
Abstract: In this paper we present a numerical method which is suitable for the integration of chemical rate equations. These equations are normally extremely stiff due to large differences in the kinetic rate coefficients. The method takes advantage of the fact that the Jacobian matrix is readily obtainable for this type of problem. Stability analysis will also be discussed in a general framework.