In this paper E-stable methods of O(h4), O(h8) and O(h12) are derived for the direct numerical integration of initial value problems of second order differential equations with exponentially decreasing solutions. Numerical results are presented for both linear and nonlinear problems. © 1985 BIT Foundations.

Ananthakrishnaiah, U.2026-02-05E-stable mBIT Numerical Mathematics, 1985, 25, 3, pp. 497-50663835https://doi.org/10.1007/BF01935370https://idr.nitk.ac.in/handle/123456789/281261985DIRECT NUMERICAL INTEGRATIONE-STABLE METHODSINITIAL VALUE PROBLEMSMATHEMATICAL TECHNIQUESIn this paper E-stable methods of O(h4), O(h8) and O(h12) are derived for the direct numerical integration of initial value problems of second order differential equations with exponentially decreasing solutions. Numerical results are presented for both linear and nonlinear problems. © 1985 BIT Foundations.