A nonlinear Dirichlet boundary value problem is approximated by an orthogonal spline collocation scheme using piecewise Hermite bicubic functions. Existence, local uniqueness, and error analysis of the collocation solution and convergence of Newton’s method are studied. The mesh independence principle for the collocation problem is proved and used to develop an efficient multilevel solution met...

In this paper, a symmetric Jacobi–Gauss collocation scheme is explored for both linear and nonlinear differential-algebraic equations (DAEs) of arbitrary index.After standard index reduction techniques, a type of Jacobi–Gauss collocation scheme with N knots is applied to differential part whereas another type of Jacobi–Gauss collocation scheme with N + 1 knots is applied to algebraic part of th...

The addition of Ru to Mn and Zr-modified Co/SiO2 catalysts, while applying different preparation orders and loading amounts, was investigated as a means of enhancing the Fischer-Tropsch synthesis reaction. The coimpregnation of Zr/SiO2 with Co, Mn and Ru gave the most attractive catalytic properties. This can be attributed to the higher dispersion of Co metal resulting from the coimpregnation o...

We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = ∑ aij(x)uxixj + ∑ bi(x)uxi + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the res...

Oxygenates formed as by-products of Fischer-Tropsch syntheses can be transformed into other Fischer-Tropsch derived oxygenates instead of treating them as unwanted chemicals. One-step direct synthesis of ethyl acetate from ethanol is feasible with the use of some heterogeneous catalysts. Despite their apparent simplicity, both transformations are discussed as targeted fields of research. Furthe...

Fischer-Tropsch synthesis: The properties of Co/zeolite bifunctional catalysts were correlated to the product distribution in synthesis. It is observed that both acidity and pore structure play a vital role primary secondary hydrocracking/isomerization reactions.

In this paper we propose a method for conducting stochastic collocation on arbitrary sets of nodes. To accomplish this, we present the framework of least orthogonal interpolation, which allows one to construct interpolation polynomials based on arbitrarily located grids in arbitrary dimensions. These interpolation polynomials are constructed as a subspace of the family of orthogonal polynomials...