ABSTRACT
It is well known that the method of quasilinearization offers an approach to obtain approximate solutions to nonlinear differential equations. See Bellman (1973), Bellman (1965) and Chan (1974). Also the method enables one to obtain lower or upper bounds for the solutions. However this is possible when the forcing term f(t,u), is uniformly convex or uniformly concave for each t ϵ [0,T]. Recently the method has been extended by Lakshmikantham (1993) to obtain two sided bounds for the solution of scalar first order ordinary differential equations. In this paper we are extending the method of quasilinearization to obtain two sided bounds for the solution of the scalar reaction diffusion equations. The method offers monotone sequences which converge quadratically to the solution of reaction diffusion equations.
