Resolving systems of ordinary differential equations in a naphtha reforming process: Comparison of laplace transform and numerical methods

Wordu, Animia Ajor; Ojong, O.E.; Okparanma, Reuben N.

doi:10.1016/j.rineng.2022.100743

Cited by 3 publications

(1 citation statement)

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“…Beyond the intrinsic complexity of solving a system of differential equations, even if the matrix coefficients are constant, the non-homogeneous term, i.e., present another layer of difficulty for the need of the particular solution. Many methods are used to solve the differential equation both analytically and numerically -for analytical solutions, Laplace and Fourier Transforms are options [1,6]; for numerical solutions, different explicit and implicit methods are used [7][8][9][10][11]. Each method presents an inherent disadvantage, such that integral transformation techniques suffer at finding the inverse transformation; while numerical methods have high computational cost and limited accuracy.…”

Section: Introductionmentioning

confidence: 99%

A systematic approach to obtain the analytical solution for coupled linear second order ordinary differential equations - Part II

Fogaça

Cardoso

2023

Preprint

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Coupled systems of second order ODEs are found in many areas, such as vibrations and electric circuits. Thus, accurate and efficient solutions are of great interest. This manuscript extends the concept of generalized integrating factor, recently introduced by the authors for one dimensional problems, to coupled n-dimensional systems of second order ODEs. The general formulation for time-varying coefficients is found and particularized to the constant coefficients. Closed-form integrating factors are obtained for the constant coefficient case under mild assumptions about the damping coefficient matrix. Analytical solutions for different types of continuous and discontinuous excitations are presented for problems with constant coefficients and proportional damping, disregarding the damping level. Examples are provided for each type of excitation studied in this manuscript. Results obtained with the proposed approach are compared to traditional numerical methods. Results show that the proposed procedure is accurate, not suffering with interpolation errors found in traditional numerical methods.

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