We propose a new Lagrange multiplier approach to construct positivity preserving schemes for parabolic type equations. The introduces space-time enforce the with Karush-Kuhn-Tucker (KKT) conditions. then use predictor-corrector class of schemes: generic semi-implicit or implicit scheme as prediction step, and correction which enforces positivity, can be implemented negligible cost. also present...

Numerical schemes based on the collisional BGK model have been developed in recent years. In this paper, we investigate the rst-order BGK schemes for the Euler equations. Particular attention is given to nd CFL-like conditions under which the schemes are positivity-preserving (i.e. density and internal energy remain nonnegative). The rst-order BGK schemes are linear combinations of collisionles...

Numerical schemes based on the collisional BGK model have been developed in recent years. In this paper, we investigate the first-order BGK schemes for the Euler equations. Particular attention is given to finding CFL-like conditions under which the schemes are positivity-preserving (i.e. density and internal energy remain nonnegative). The first-order BGK schemes are linear combinations of col...

The Cox-Ingersoll-Ross (CIR) interest rate model is one of the most celebrated models in financial industry. The CIR interest rate model always has been the focus of study in mathematical finance litrature [2] as well as in the financial industry. It is also the area of interest in numerical science litrature [3 4 6 8 9 10 13 14 15 16 20] because of its non-explicit analytical solution. Signifi...

A piecewise rational cubic spline [5] has been used to visualize the positive data in its natural form. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters in the description of a rational cubic have been constrained in such a way that they preserve the shape of the positive data in the view of positive curve. As far as visual smoothness is ...