2014/02/09 by Mustafa Riza, Riza, Mustafa, Buğçe Eminağa +1
Decision Sciences · Mathematics · Physics and Astronomy · #34K25 #65L06 #FOS: Mathematics #General Mathematics (math.GM) #Model Reduction and Neural Networks #Numerical methods for differential equations #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1402.2877
openalex publication_date 2014/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The properties of the Bigeometric or proportional derivative are presented and discussed explicitly. Based on this derivative, the Bigeometric Taylor theorem is worked out. As an application of this calculus, the Bigeometric Runge-Kutta method is derived and is applied to academic examples, with known closed form solutions, and a sample problem from mathematical modelling in biology. The comparison of the results of the Bigeometric Runge-Kutta method with the ordinary Runge-Kutta method shows that the Bigeometric Runge-Kutta method is at least for a particular set of initial value problems superior with respect to accuracy and computation time to the ordinary Runge-Kutta method.