128 research outputs found
Numerical Solution of Parabolic Equations by the Box Scheme
No full textThe box scheme proposed by H. B. Keller is a numerical
method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic equations. Von Neumann stability is shown to hold for the box scheme combined
with the method of fractional steps to solve the two-dimensional heat equation. Computations were performed on Burgers' equation with three different initial conditions, and Richardson extrapolation is shown to be effective.</p
Thermodynamic Insights on the structure‐property relationships in substituted benzenes: are the pairwise interactions in tri‐substituted methyl‐nitro‐benzoic acids still valid?
No full textA comprehensive experimental thermochemical study of nine methyl‐substituted nitrobenzoic acids was carried out, leading to the final standard molar enthalpies of formation in the gas phase. The combustion energies were measured using high‐precision combustion calorimetry, and the enthalpies of formation of the crystal phase were derived. The sublimation enthalpies were obtained from the vapor pressure‐temperature dependencies measured using the classic Knudsen effusion mass loss and the transpiration methods. The standard molar enthalpies of vaporisation were derived from the temperature dependence of the mass‐loss rates measured using the non‐isothermal thermogravimetry. The thermal behaviour, including melting temperatures and standard molar enthalpies of fusion, was investigated by DSC. The high‐level quantum chemical G* methods were used for the mutual validation of the experimental and theoretical gas phase enthalpies of formation of methyl‐substituted nitrobenzoic acids. The consistent set of experimental properties at the reference temperature T = 298 K was evaluated and recommended for thermochemical calculations. The pairwise interactions of the substituents on the benzene ring were derived from nitro‐toluenes, methyl‐benzoic acids and nitro‐benzoic acids available in the literature, and the additivity of the contributions when three substituents are placed simultaneously in the benzene ring was discussed
The Method of Weak Approximation and the Construction of the Solution of the Cauchy Problem in Banach Space
No full textDie Zwischenschrittmethode zur Lösung mehrdimensionaler Probleme der mathematischen Physik
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The method of fractional steps: the solution of problems of mathematical physics in several variables
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Application of the Method of Fractional Steps to Boundary Value Problems for Laplace’s and Poisson’s Equations
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