# Comparison of some implicit and explicit schemes for open channel flow equations

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## Abstract

When deciding whether to employ explicit or implicit approach in numerical approximation of open channel flow equations one has to bear in mind that explicit methods are generally easier to program, and require less computational effort per each time step than implicit methods. Explicit methods solve for one point at a time in certain time step - that is, one equation and one unknown. The main drawback of the explicit approach is that the unknown node must be within the zone of dependency of the nodes that are used to approximate the derivatives at the known time line – otherwise, the method will be unstable. Therefore, maximal time step is bound by Courant Friedrichs Lewy (CFL) condition. Implicit methods solve for the unknowns in a domain simultaneously, requiring solution of simultaneous algebraic equations. The advantage is that matrix of a linear system to be solved at each time level has its argum