Numerical Solution of the Problem of Sediment Transport Based on an Improved Version of the Alternating-Triangular Method with Improved Spectral Estimates

Sediment transport is one of the main processes that determine the magnitude and rate of deformation of the bottom surfaces of water bodies. The study of sediment transport processes, increasing the accuracy and reliability of scenarios of their behavior under certain conditions requires specialists to constantly improve existing methods of mathematical and numerical modeling. In this paper, we consider methods for solving two-dimensional boundary value problems and nonlinear equations that describe these processes, based on the iterative alternating-triangular method. A modification of this method is constructed, which, under a special restriction on the source function, requires \(n_0 \left( \varepsilon \right) = O\left( {1/\sqrt[4]{\left\| h \right\|}} \right)\) iterations. An improved estimate of the parameter for the alternating-triangular method is obtained due to a separate consideration of the diagonal component of the problem matrix, which made it possible to asymptotically halve the number of required iterations. Improved spectral estimates and results of numerical experiments are presented.