An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems: a computational study

An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\cal N})$ operations where ${\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties

Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components

Nonthermal Plasma Microreaction Engineering for Gas and Liquid Processing

Atmospheric pressure plasma is non-thermal at millimeter to micrometer separations. It represents an alternative low exergy initiator of many chemical reactions. In many instances heat, light or sound are not efficient providers of the necessary energy to overcome chemical activation barriers. The focus of this research is applying dc nonthermal plasma for gas and liquid chemical processing. The sub-millimeter dimensions offered by microtechnology are utilized to activate the majority of the gas or liquid stream. This enhances conversion, product yield and process efficiency. The first reported sustained dc emission from arrays of micro-emitter electrodes is contained within this thesis. This is the first formation of constant dc microcorona fields at atmospheric pressure in air and hydrocarbon gases. Methane is chemically converted in several microchannel devices to higher value products. A discovery that may lead to improved recoverability of stranded natural gas in our current energy cycle. Methane conversion to either C₂ or C₃ hydrocarbons of up to 80% with high selectivity are demonstrated. A finite element chemical engineering mathematical model for the hydrocarbon coupling reaction is developed. Plasma microreactors can also dry reform methane to synthesis gas. The feasibility of microplasma carbon dioxide dry reforming in a microreactor with a dc sustaining voltage under 1kV has been demonstrated. More than 60% conversion is achieved in the unoptimized reactor with nearly complete selectivity to synthesis gas. A plasma microchannel device can completely degrade representative trace toxic organic contaminants in a single pass. Rhodamine B is a colorimetric dye used as an example organic compound. A G[subscript 50%] factor, which represents the energy required to remove half of the starting contaminant, is tabulated for both a batch reactor and microchannel device. The plasma electrochemical activation of advanced oxidation chemistry converts from E-6 to E-11 moles per joule of input energy