This paper displays an efficient numerical technique of realizing mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic chemical reaction.At a steady-state solution for a...This paper displays an efficient numerical technique of realizing mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic chemical reaction.At a steady-state solution for an adiabatic rounded reactor,the model can be diminished to a conventional nonlinear differential equation which converts into a system of the nonlinear equation that can proceed numerically utilizing Newton’s iterative method.An operational matrix of coordination is derived and is utilized to decrease the model for an adiabatic tubular chemical reactor to an arrangement of algebraic equations.Simple execution,basic activities,and precise arrangements are the fundamental highlights of the proposed wavelet technique.The numerical solutions attained by the present technique have been contrasted and compared with other techniques.展开更多
A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods wa...A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data with and without random noise to invert and compare it with the known analytical inverse. Thus it is a good method for applying to experimental intensities distorted by noise.展开更多
文摘This paper displays an efficient numerical technique of realizing mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic chemical reaction.At a steady-state solution for an adiabatic rounded reactor,the model can be diminished to a conventional nonlinear differential equation which converts into a system of the nonlinear equation that can proceed numerically utilizing Newton’s iterative method.An operational matrix of coordination is derived and is utilized to decrease the model for an adiabatic tubular chemical reactor to an arrangement of algebraic equations.Simple execution,basic activities,and precise arrangements are the fundamental highlights of the proposed wavelet technique.The numerical solutions attained by the present technique have been contrasted and compared with other techniques.
基金Supported by the National Natural Science Foundation of China(11601076)the Youth Science Foundation of Jiangxi Province(20151BAB21100420151BAB211012)
文摘A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data with and without random noise to invert and compare it with the known analytical inverse. Thus it is a good method for applying to experimental intensities distorted by noise.
