The purpose of this work is to introduce a new idea how avoid the factorization large matrices during solution stiff systems ODEs. Starting from general form an explicit linear multistep method we suggest adaptively choose its coefficients on each integration step in order minimize norm residual implicit BDF formula. Thereby reduce number unknowns n O(1), where dimension ODE system. We call typ...

In this paper, some approximate analytical methods are reviewed, including the variational iteration method and homotopy perturbation method. Based on ideas of two methods, a new for solving class system Fredholm integral equations second kind is proposed. Some examples given to show simple solution process accuracy each The emphasis review paper focuses Ji-Huan He?s unapproachable mathematics ...

For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool f...