Application Of Classical Formulas Research Articles

Numerical differentiation on the Bakhvalov mesh in the presence of an exponential boundary layer

The question of the application of formulas of the numerical differentiation of functions in the presence of the exponential boundary layer is investigated. The problem is that the application of classical formulas, wich are based on the differentiation of the Lagrange polynomial on the uniform mesh in this case leads to significant errors. It is proposed to study the formulas for derivatives on the Bakhvalov mesh, which is widely used in the construction of difference schemes for singularly perturbed problems. It is proved that applying of classical difference formulas for derivatives on a Bakhvalov mesh have error estimate that is uniform with respect to a small parameter. The results of numerical experiments are presented.

Application of classical formula in treatment of diabetes

The application of classical formula in the treatment of diabetes has a long history. Zhang Zhongjing set up a special chapter on consumptive thirst in Synopsis of the Golden Chamber,listing Baihu Jia Renshen Decoction for exuberant heat in the lung and stomach,dual deficiency of Qi and Yin syndrome,and Shenqi Pills for kidney Qi deficiency syndrome. However,the clinical application is not limited to them. In this study,formulas of Huanglian,Dahuang,Chaihu,Gualougen,Lingzhu,Huangqi and Dihuang are listed as the main therapeutic methods for diabetes mellitus,with effects in clearing heat,dredging the bowels and purging turbid,clearing depression and dispersing knots,nourishing Yin and quenching thirst,invigorating spleen and draining dampness,supplementing Qi and tonifying deficiency,nourishing Yin and tonifying kidney,which have the advantages for the treatment of diabetes and its complications. Based on accurate differentiation of symptoms and signs,consideration shall be given to both " of diseases and syndromes",while emphasis shall be given to the " main symptoms",so as to flexibly apply classical formula and expand the scope of application.