Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations (Mississippi State University, 1997); Electronic Journal of Differential Equations
The method of quasilinearization, coupled with the method of upper and lower solutions, is applied to a boundary value problem for an ordinary differential equation with impulse that has a unique solution. The method generates sequences of approximate solutions which converge monotonically and quadratically to the unique solution. In this work, we allow nonlinear terms with respect to velocity; in particular, Nagumo conditions are employed.
Doddaballapur, Vidya; Eloe, Paul W.; and Zhang, Yongzhi, "Quadratic convergence of approximate solutions of two-point boundary value problems with impulse" (1998). Mathematics Faculty Publications. 95.