Advances in Chemical Physics: Singular Perturbation Problems

The Matching process for Asymptotic ideas in Chemical Physics difficulties by means of A. M. Il'in, L. A. Kalyakin, and S. I. Maslennikov

Singularly Perturbed issues of Boundary and inside Layers: idea and alertness by means of V. F. Butuzov and A. B. Vasilieva

Numerical equipment for Singularly Perturbed Boundary price difficulties Modeling Diffusion procedures by means of V. L. Kolmogorov and G. I. Shishkin

a big addition to the Advances in Chemical Physics sequence, this quantity makes to be had for the 1st time in English the paintings of major Russian researchers in singular perturbation idea and its software. because boundary layers have been first brought via Prandtl early during this century, swift advances were made within the analytic and numerical research of those phenomena, and nowhere have those advances been extra amazing than within the Russian college of singular perturbation conception. the 3 chapters during this quantity deal with numerous elements of singular perturbations and their numerical resolution, and characterize the very best paintings performed during this region:
* the 1st bankruptcy, "The Matching strategy for Asymptotic recommendations in Chemical Physics Problems," is anxious with the research of a few singular perturbation difficulties that come up in chemical kinetics. during this bankruptcy the matching strategy is utilized to discover asymptotic ideas to a couple dynamical platforms of normal differential equations whose suggestions have multiscale time dependence.
* the second one bankruptcy, "Singularly Perturbed issues of Boundary and inside Layers: conception and Application," deals a finished evaluate of the speculation and alertness of asymptotic approximations for lots of other kinds of difficulties in chemical physics ruled through both traditional or partial differential equations with boundary and inside layers.
* The 3rd bankruptcy, "Numerical tools for Singularly Perturbed Boundary price difficulties Modeling Diffusion Processes," discusses the numerical problems that come up in fixing the issues defined within the first chapters, and proposes rigorous standards for opting for even if a numerical procedure is passable for such difficulties. tools pleasing those standards are then built and utilized to procure numerical options to a number of pattern problems.

well timed, authoritative, and worthwhile to researchers in all components of chemical physics, Singular Perturbation difficulties in Chemical Physics is a vital resource.Content:

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Additional info for Advances in Chemical Physics: Singular Perturbation Problems in Chemical Physics: Analytic and Computational Methods, Volume 97

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D. 29) are applied to find K, and Wi. 12) on the time scale I1 due to the matching condition. 32) Experimental results can be treated in two ways. 1. The kinetic curve, plotted for varying concentrations of the peroxide radical, is a straight line with respect to the coordinates (see Fig. 4) l n [ ( l + d ) / ( 1 - d ) ] - 1/d+ T The effective rate constant is determined by the slope of the resulting straight line. 33) By following Eqs. 35) Thus, starting from the value [InH], and the known value 2K,, we can find K7 and W,.

Contrast Structures in Partial Differential Equations A. Step-Type Solutions in the Noncritical Case B. Step-Type Solutions in the Critical Case C. Spike-Type Solutions D. Applications 1. Phase Transition Models 2. Fisher’s Equation IX. Mathematical Model of Combustion in the Case of Autocatalytic Reaction A. Statement of the Problem B. Construction of the Leading Terms of the Asymptotic Expansion C. Construction of Subsequent Terms of the Asymptotic Expansion D. Physical Interpretation of the Asymptotics of the Solution X.

The Main Result D. The Problem for a Thin Three-Dimensional Rod E. The Case of a Small Thermal Diffusion Coefficient F. The Problem of Thermoelasticity in Thin Bodies Acknowledgment! References I. A. INTRODUCTION Singularly Perturbed Differential Equations Differential equations are often used as mathematical models describing processes in physics, chemistry, and biology. In the investigation of a number of applied problems, an important role is played by differential equations that contain small parameters at the highest derivatives.

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