Numerical Solution of Some Stiff Systems Arising in Chemistry Via Taylor Wavelet Collocation Method

This paper presents the innovative Taylor wavelet collocation method (TWCM) for the stiff systems arising in chemical reactions. In this technique, first, we generated the functional matrix of integration (FMI) for the Taylor wavelets. Using this FMI, the Taylor wavelet collocation method is proposed to obtain the numerical approximation of stiff systems in the form of a system of ordinary differential equations (SODEs). This method converts the SODEs into a set of algebraic equations, which can be solved by the Newton–Raphson method. To demonstrate the simplicity and effectiveness of the presented approach, numerical results are obtained. Graphs and tables illustrate the created strategy's effectiveness and consistency. Illustrative examples are examined to demonstrate the performance and effectiveness of the developed approximation technique, and a comparison is made with the current results. Results reveal that the newly selected strategy is superior to previous approaches regarding precision and effectiveness in the literature. Most semi-analytical and numerical methods work based on controlling parameters, but this technique is free from controlling parameters. Also, it is easy to implement and consumes less time to handle the system. The suggested wavelet-based numerical method is computationally appealing, successful, trustworthy, and resilient. All computations have been made using the Mathematica 11.3 software. The convergence of this strategy is explained using theorems.