In this paper, the Chebyshev wavelet method, constructed from the Chebyshev polynomial of the first kind is proposed to numerically simulate the single-phase flow of fluid in a reservoir. The method was used together ...In this paper, the Chebyshev wavelet method, constructed from the Chebyshev polynomial of the first kind is proposed to numerically simulate the single-phase flow of fluid in a reservoir. The method was used together with the operational matrices of integration which resulted in an algebraic system of equations. The system of equation was solved for the wavelet coefficient and used to construct the solutions. The efficiency and accuracy of the method were demonstrated through error measurements. Both the root mean square and the maximum absolute error analysis used in the study were within significantly close range. The Chebyshev wavelet collocation method subsequently was observed to closely approximate the analytic solution to the single phase flow model quite well.展开更多
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
文摘In this paper, the Chebyshev wavelet method, constructed from the Chebyshev polynomial of the first kind is proposed to numerically simulate the single-phase flow of fluid in a reservoir. The method was used together with the operational matrices of integration which resulted in an algebraic system of equations. The system of equation was solved for the wavelet coefficient and used to construct the solutions. The efficiency and accuracy of the method were demonstrated through error measurements. Both the root mean square and the maximum absolute error analysis used in the study were within significantly close range. The Chebyshev wavelet collocation method subsequently was observed to closely approximate the analytic solution to the single phase flow model quite well.
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.
