Showing papers on "Autonomous system (mathematics) published in 1963"
01 Jan 1963
TL;DR: In this article, a method for computing a periodic solution of the van der pol equation of a general autonomous system is devised. But this method seems to be inconvenient as it reveals the singular behavior near the x-axis for the closed orbits of the system.
Abstract: Publisher Summary This chapter discusses the numerical study of periodic solutions of the van der pol equation. In the chapter, a method for computing a periodic solution of a general autonomous system is devised. This method seems to be inconvenient as it reveals the singular behavior near the x-axis for the closed orbits of the system. In computation, the results are obtained accurately by devising a new method of step-by-step numerical integration for the system. This method is well suited to the present problem of computing values of the periodic solution of a general autonomous system, which are quite good in spite of the large number of steps. This is because of the fact that the truncation errors and the rate of growth of round-off and truncation errors are both smaller in this new methodthan the usual multi-step formulas.
20 citations