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The basic equation of Gradually Varied Flow (GVF) describes the variation of water depth with flow process. Several methods have been developed for numerical solution of the water surface profile in GVF and one of the challenges of numerical integration is determining the appropriate integration spatial step size. In this paper a novel Adaptive Newton-Raphson method is developed for numerical solution of the GVF equation. In this method the spatial steps are determined by using error estimationdoi:10.22055/jise.2017.14367 doaj:d39c220981534758927d08e25c627485 fatcat:5nse5fdia5enpcaa26m543nqqi