An extension of quasilinearization to reaction diffusion equations with fixed moments of impulses

In this paper the method of quasilinearization has been extended to reaction diffusion equations with fixed moments of impulses when the forcing function is the sum of a convex and a concave function. The extension of quasilinearization has been done in such a way that the iterates are linear as in quasilinearization method and yet have quadratic convergence as in quasilinearization method. The quadratic convergence has been achieved by using the comparison theorem of reaction diffusion equations with fixed moments of impulses with ordinary differential equations with fixed moments of impulses. Also results related to coupled upper and lower solutions of all possible varieties are developed for reaction diffusion equations with fixed moments of impulses.