The present work is inspired by the recent developments in laboratory experiments made on chips, where culturing of multiple cell species was possible. model based coupled reaction-diffusion-transport equations with chemotaxis and takes into account interactions among populations possibility drug administration for testing effects. Our effort devoted to development a simulation tool that able r...

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high order positivity-preserving finite difference WENO methods for the ideal magnetohydrodynamic (MHD) equations. Our schemes, under the constrained transport (CT...

A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...

Maximum principle or positivity-preserving property holds for many mathematical 5 models. When the models are approximated numerically, it is preferred that these important prop6 erties can be preserved by numerical discretizations for the robustness and the physical relevance of 7 the approximate solutions. In this paper, we investigate such discretizations of high order accuracy 8 within the ...