A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution

We present a new algorithm to solve the basic stream power equation, which governs channel incision and landscape evolution in many geomorphic settings. The algorithm is highly efficient because computation time increases linearly with the number of points used to discretize the landscape and is ideally suited to parallelization. It is also unconditionally stable because it uses an implicit scheme for the time integration of the landscape evolution equation, which means that large time steps can be used without sacrificing accuracy. In this paper we describe the algorithm and present results that demonstrate its efficiency and accuracy.

► We propose a new, very efficient method to solve the stream power law. ► The method is order N (number of nodes). ► It is fully implicit. ► It is parallel. ► It can be used to solve very large problems (10^8 nodes).