An innovative Vieta–Fibonacci wavelet collocation method for the numerical solution of three-component Brusselator reaction diffusion system of fractional order
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Abstract
The research article presents a novel approach for the numerical solution of three-component time fractional order Brusselator reaction-diffusion system using the innovative Vieta–Fibonacci wavelet and collocation method. The proposed method involves the derivation of operational matrices for both integer and fractional order derivatives, enable the accurate and efficient computation of the system. The existence, uniqueness of solution and Ulam–Hyers stability of the model are rigorously discussed. Furthermore, a comprehensive convergence analysis of the Vieta–Fibonacci wavelet method is presented, which demonstrates its effectiveness in approximating the fractional derivative of the Brusselator system. The numerical experiments showcase the superior performance of the method in terms of accuracy and computational efficiency. The application of the Vieta–Fibonacci wavelet method to the three-component fractional order Brusselator reaction-diffusion system marks a significant advancement in the field of computational mathematics. The successful implementation of the Vieta–Fibonacci wavelet method signifies a significant advancement in solving fractional-order reaction-diffusion problems.
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The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
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