A NUMERICAL SCHEME FOR Q-DIFFERENTIAL EQUATIONS

This paper presents the development and application of an innovative numerical technique, the q-Taylor method, for solving q-initial value problems (q-IVPs) arising within the framework of q-calculus. The study begins by extending the classical Taylor series to the q-calculus setting, thereby establishing the theoretical foundation of the proposed method. A comprehensive mathematical analysis is carried out to examine the fundamental properties and convergence behavior of the q-Taylor method. The technique is then applied to two illustrative examples, with MATLAB employed as the computational tool for implementation. Two test problems are used to evaluate the method’s accuracy and efficiency. The results are compared with existing numerical approaches to highlight the strengths and potential limitations of the proposed method.