A fourth order method for a singular two-point boundary value problem

Recently, Chawla et al. described a second order finite difference method for the class of singular two-point boundary value problems:

Two-step fourth orderP-stable methods for second order differential equations

A family of symmetric (hybrid) two-step fourth order methods is derived fory'=f(x,y). We then show the existence of a sub-family of these methods which when applied toy'=– ² y, real, areP-stable. We also note that a general (order) symmetric two-step method isP-stable iff it is unconditionally stable.     

A sixth order tridiagonal finite difference method for non-linear two-point boundary value problems

We present a new sixth order finite difference method for the second order differential equationy=f(x,y) subject to the boundary conditionsy(a)=A,y(b)=B. An interesting feature of our method is that each discretization of the differential equation at an interior grid point is based onfive evaluations off; the classical second order method is based on one and the well-known fourth order method of Noumerov is based on three evaluations off. In case of linear differential equations, our finite difference scheme leads to tridiagonal linear systems. We establish, under appropriate conditions, the sixth order convergence of the finite difference method. Numerical examples are considered to demonstrate computationally the sixth order of the method.     

An eighth order tridiagonal finite difference method for nonlinear two-point boundary value problems

We present an eighth order finite difference method for the second order nonlinear boundary value problemy=f(x, y), y(a)=A, y(b)=B; the method iseconomical in the sense that each discretization of the differential equation at an interior grid point is based on seven evaluations off. For linear differential equations, the scheme leads to tridiagonal linear systems. We showO(h ⁸)-convergence of the method and demonstrate computationally its eighth order.     

Molecular weight distribution studies. I. Radiation-induced polymerization of liquid α-methylstyrene

The concentration of water in purified and BaO-dried α-methylstyrene was found to be 1.1 × 10^?4M. The radiation-induced bulk polymerization of the α-methylstyrene thus prepared was studied in the temperature range of ?20°C to 35°C. The polymerization rate varied as the 0.55 power of the dose rate. The theoretical molecular weights and molecular weight distribution were calculated from a proposed kinetic scheme and these values were then compared with those found experimentally. The agreement between these two was reasonably close, and therefore it was concluded that, from the molecular weight distribution point of view, the proposed kinetic scheme for the cationic polymerization of α-methylstyrene is an acceptable one. The rate constant for chain transfer to monomer k_f changed with temperature and was found to be responsible for the decrease in the molecular weight of the polymer with increase in temperature. k_f and k_p at 20°C were found to be 0.95 × 10⁴ l./mole-sec and 0.99 × 10⁶ l./mole-sec, respectively.     

Determination of the sulfur components of gasoline streams by capillary column gas chromatography with sulfur chemiluminescence detection

A method using a sulfur chemiluminescence detector (SCD) has been developed for the qualitative and quantitative determination of sulfur components in stabilized gasoline-range process streams, including blended gasolines containing between 1 and > 4000 ppm total sulfur. The detection limit per sulfur component was approximately 50 ppb. On-column injection was employed for optimum precision and accuracy. A new probe material was found which did not soften under FID operating conditions. A new method, using a hydrogen sulfide permeation tube, was developed for rapid alignment of the probe in the FID.     

Thermodynamic studies of some binary mixtures containing a self-associated component. II. Excess volumes of some mixtures of tetrahydrofuran with alcohols

Excess volumes of mixing, V^E, for binary mixtures of tetrahydrofuran (THF) with methanol, ethanol, n-butanol, tert-butanol, 2-bromoethanol and ethylene glycol have been determined from the experimental density measurements at 298.15 K over the entire composition range. The V^E data follow the order: ethylene glycol < 2-bromoethanol < methanol < ethanol < n-butanol < tert-butanol. The results have been explained in terms of self-association and the hydrogen bond-donating abilities of alcohols.     

Depression in the cloud point of Tween in the presence of glycol additives and triblock polymers

Cloud point (C_P) measurements of Tween 20 and Tween 80 were carried out in the presence of various glycol oligomers and triblock polymers (TBP). The cloud points of both Tween 20 and 80 decrease in the presence of both types of additives. Among the glycol oligomeric additives, ethylene glycol monobutyl ether was found to reduce the C_P maximum. An increase in the repeating units of polymeric glycol additives leads to a decrease in C_P. Reduction in the C_P in the presence of TBP depends upon the increase in hydrophobic/hydrophilic ratio among the polypropylene to polyethylene units.     

One Pot One Step Photoconversion of Pulvinic Acid Dilactone to p-Methoxyvulpinic Acid

The utility of singlet oxygen-methanol as a reagent for nuclear methoxylation of complex organic natural products is illustrated by a one pot one step photoconversion of pulvinic acid dilactone to p-methoxyvulpinic acid. The study is important from biogenetic considerations.