Modified line-by-line method for difference elliptic equations (Q1571248)

The author considers a modified line-by-line method for solving difference elliptic equations that arise in numerical approximation of two-dimensional equations of viscous fluid dynamics and heat or mass transfer. The algorithm is based on the scalar technique of the alternating direction method. Convergence is improved by increasing the implicit part of the algorithm's implementation, taking into account the boundary condition in the transverse direction to a grid lines and decreasing the norm of the iterated expression.