Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The...

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

Functional polymers bear specified chemical groups, and have specified physical, chemical, biological, pharmacological, or other uses. To adjust the properties while keeping material usage low, a method for direct synthesis of functional polymers is indispensable. Here we show that various functional polymers can be synthesized by in situ cross-linked polymerization/copolymerization. We demonst...

In this work we develop a method of straight lines for a one-dimensional Bingham problem. A Bingham fluid has viscosity properties that produce a separation into two regions, a rigid zone and a viscous zone. We propose a method of lines with the time as a discrete variable. We prove that the method is well defined, a monotone property, and a convergence theorem. Behavior of the numerical soluti...

determination of price of lost property is faced with two difficulties: on the one hand, property price is variable from time to time so it is necessary to determine the price of the item in which time must be considered? on the other side question of devaluation of money is raised. whether the agent of the loss is responsible for this or she/he is merely responsible for the value of property i...

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, rob...

The current aim of our research work is to isolate bio-polymer from fresh rhizomes of Zingiber officinale & to evaluate its retardibility by formulating microdwarfs containing nimesulide as a model drug. The bio-material was isolated by a simplified method. Six different bio-micro dwarf formulations were prepared using isolated bio-material as a retardant. The formulated microcapsules were eval...

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the c...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...