Cubic and quartic convergence for first-order periodic boundary-value problems
Abbreviated Journal Title
J. Optim. Theory Appl.
existence; periodic boundary-value problems; upper and lower solutions; convergence; quasilinearization; Operations Research & Management Science; Mathematics, Applied
In this paper, the results of Lakshmikantham et al. (Ref. 1) for first-order periodic boundary-value problems are extended, by using the extended method of quaislinearization and rapid convergence for initial-value problems of Mohapatra et al. (Ref 2). Also, it is shown that monotone sequences converge cubically to the unique solution when the forcing function in the differential equation is 2-hyperconvex and converge quartically when the forcing function is 3-hyperconvex. Several other generalizations of the problem are also presented.
Journal of Optimization Theory and Applications
"Cubic and quartic convergence for first-order periodic boundary-value problems" (1998). Faculty Bibliography 1990s. 2370.