Numerical Differentiation and Integration in Chemical Kinetics.

Numerical Solution Methods in Stochastic Chemical Kinetics

New Iterative Methods for Interpolation, Numerical Differentiation and Numerical Integration

Through introducing a new iterative formula for divided difference using Neville's and Aitken's algorithms, we study new iterative methods for interpolation, numerical differentiation and numerical integration formulas with arbitrary order of accuracy for evenly or unevenly spaced data. Basic computer algorithms for new methods are given.

Automatic differentiation of numerical integration algorithms

Automatic differentiation (AD) is a technique for automatically augmenting computer programs with statements for the computation of derivatives. This article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations (ODEs), in particular, the ramifications of the fact that AD is applied not only to the solution of such an algo...

Numerical Investigations of Chemical Kinetics for Methane Catalysis and Pyrolysis

In the framework of the active and regenerative cooling of hypersonic and space structures, a kinetic mechanism should be proposed to investigate numerically the fuel pyrolysis and the coke formation with a possible surface effect (catalytic reactions). This chemical mechanism should be suitable for Computational Fluid Dynamics approach (limited number of species and reaction). For this purpose...

Approximation, Numerical Differentiation and Integration Based on Taylor Polynomial

We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remainder in Taylor formula by least concave majorant of the modulus of continuity of the n−th derivative of an n−times differentiable function. Our quantitative estimates are special applications of a mo...