Difference Methods and Deferred Corrections for Ordinary Boundary Value Problems

Compact as possible difference schemes for systems of nth order equations are developed. Generalizations of the Mehrstellenverfahren and simple theoretically sound implementations of deferred corrections are given. It is shown that higher order systems are more efficiently solved as given rather than as reduced to larger lower order systems. Tables of coefficients to implement these methods are included and have been derived using symbolic computations

Local Sensitivity Analysis of Kinetic Models for Cellulose Pyrolysis

Abstract: The first and nth order kinetic models are usually used to describe cellulose pyrolysis. In this work, the local sensitivities of the conversion and derivative conversion with respect to the frequency factor, the logarithm of the frequency factor, the activation energy and the reaction order for the first and nth order kinetic models are calculated by using the finite difference method. The results show that the sensitivities of the first and nth order kinetic models with respect to the activation energy and the logarithm of the frequency factor are significant, while the frequency factor and the reaction order affect the nth order kinetic model slightly. Compared with the frequency factor, the natural logarithm of the frequency factor is a better choice in the parameter estimation of the first and nth order kinetic models. Graphical Abstract: [Figure not available: see fulltext.

Discretisations of higher order and the theorems of

We study discrete functions on equidistant and nonequidistant infinitesimal grids. We consider their difference quotients of higher order and give conditions for their nearequality to the corresponding derivatives. Important tools are nonstandard notions of regularity of higher order, and the formula of Fa`a di Bruno for higher order derivatives and a iscrete version of it. As an application of such transitions from the discrete to the continuous we extend the DeMoivreLaplace Theorem to higher order: nth order difference quotients of the binomial probability distribution tend to the corresponding nth order partial differential quotients of the Gaussian distribution

The Construction of Finite Difference Approximations to Ordinary Differential Equations

Finite difference approximations of the form Σ^(si)_(i=-rj)d_(j,i)u_(j+i)=Σ^(mj)_(i=1) e_(j,if)(z_(j,i)) for the numerical solution of linear nth order ordinary differential equations are analyzed. The order of these approximations is shown to be at least r_j + s_j + m_j - n, and higher for certain special choices of the points Z_(j,i). Similar approximations to initial or boundary conditions are also considered and the stability of the resulting schemes is investigated

The Cauchy problem for a fourth order parabolic equation by difference methods

Thesis (Ph.D.)--Boston UniversityThis paper deals with the solution of parabolic partial differential equations by difference methods. It is first concerned with obtaining certain basic results for the nth order equation... This enables one to exhibit a stable difference equation compatible with (5). Once assured of the existence of such an equation, it is employed in proving an existence theorem for a solution of the differential equation. The theorem states that if the coefficients a;(x,t) and the function d(x, t) in (5), and the function f(x) in:(2) possess a sufficient number of uniformly continuous and bounded derivatives in R, and a0(x,t) is negative and bounded away from zero, then there exists a solution of (5), (2) possessing a certain number of uniformly continuous and bounded derivatives. [TRUNCATED