Abstract
The purpose of this research is to impose a semi-analytical method called the iterative method to the chemical kinetics system, which appears in the form of a system of ordinary differential equations. To test the accuracy of the standard iterative method, we have applied the classical fourth-order Runge–Kutta method and the iterative method to the chemical kinetics system. It is significantly notable that approximate analytical precisions of standard iterative method made a high agreement with those obtained from the fourth-order Runge–Kutta technique. Numerical outputs and solution procedures indicate that iterative method can be easily applicable to a large class of scientific numeric applications with high accuracy.
Highlights
Differential equations play a prominent role in various fields such as physics, chemistry, biology, mathematics, engineering, and other disciplines.[1,2,3,4,5,6] There are few phenomena in different fields of science occurring linearly
This paper is organized as follows: in “The solution approach based on the iterative method” section, we provided the outline of the solution approach based on the IM
There are no exact solutions for the non-linear chemical kinetics systems of ordinary differential equations (ODEs)
Summary
Differential equations play a prominent role in various fields such as physics, chemistry, biology, mathematics, engineering, and other disciplines.[1,2,3,4,5,6] There are few phenomena in different fields of science occurring linearly. Its exact solution might be too complex to use for a practical application, or sometimes, it is impossible to obtain its exact solution. To overcome this difficulty, there are numerous methods undertaken to find out numerical as well as analytical series solutions for nonlinear problems: Variational Iteration Method (VIM),[7] Adomian Decomposition Method (ADM),[8] Homotopy Analysis Method (HAM),[9] Harmonic Balance Method (HBM),[10] Homotopy-Perturbation Method (HPM),[11,12] Haar wavelet quasilinearization method,[13] and Haar wavelet operational matrix method[14] are some proven instances. The nonlinear analytical techniques are fast developing, they still do not completely satisfy the mathematicians and engineers
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