NUMERICAL SOLUTIONS OF BIGEOMETRIC INITIAL VALUE PROBLEMS USING THE BIGEOMETRIC RUNGE KUTTA METHOD

In many studies based on Bigeometric Calculus, an approximation to the BigeometricTaylor series is used without knowing the correct version. The reason for that can be seen easily inthe proof of the Bigeometric Taylor Series presented in the current paper. Based on this Taylor seriesthe Bigeometric Runge-Kutta method is derived explicitly. As the Runge-Kutta method is based onthe first derivative, it is not surprising that the coefficients and parameters in the Bigeometric RungeKutta behave according to the Butcher Tableau. The convergence and stability tests are also appliedto the Bigeometric Runge-Kutta. Application of the Bigeometric Runge-Kutta method to problemswith known closed form solutions show the superiority of this method for a certain family of problemscompared to the one in Newtonian calculus. Furthermore, the Bigeometric Runge-Kutta method isapplied to mathematical modelling in biology and the Bigeometric R¨ossler attractor, showing thegeneral applicability of the method