A STABLE AND HIGH ACCURACY MULTISTEP NUMERICAL DIFFERENTIATION SCHEME FOR NONLINEAR THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS ARISING IN CHEMICAL REACTION MODELING
This investigation presents an innovative method for solving 3 rd order ODEs that have predetermined beginningconditions. This method is a numerical methodology that involves multiple steps. The objective of this techniqueisto increase the stability and precision of numerical approximations. When it comes to systems that are complexandnonlinear, where it is difficult to find analytical solutions, this is of particular importance. When the stepsizeparameter r is equal to 1, we provide a straightforward formula for the operation. As a result, it is simple and quickto utilise in calculations. Our process for ensuring that the technique works is to conduct numerical tests by solvingafew selected 3 rd order ODEs and then comparing outcomes to known precise solutions. The process of computationfor this approach is more efficient since it necessitates fewer steps, and it is also more precise, which is the onlyadvantage that this technique has, as demonstrated by the comparison. This study contributes a practical computation tool for modelling complex chemical reaction pathways and supports Sustainable Development Goal associated with industry, innovation & infrastructure by promoting reliable numerical techniques for industrial andscientific simulations. The results of the investigation show that the multistep strategy that has been recommendedisa reliable and successful option for dealing with higher-order initial value problems in a variety of engineeringandscientific fields.
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