The classical Ka?anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates given approximation by solving linear problem in each step. Based on this observation, we introduce modified Ka ? anov , which allows (adaptive) damping, and, thereby, to derive new convergence analysis under more general assumptions and wider range a...

A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

The Richards equation is widely used in the simulation of unsaturated flow and related fields. In numerical solution process, finite volume method can be to carry out discretization, Picard for iterative solution. However, order obtain a more reliable solution, space step size conventional uniform grid often small. Especially under some unfavorable conditions, such as infiltration into dry soil...