Accuracy of Fifth-Order Improved Runge-Kutta Method for Handling Hyperchaotics Finance Systems

Abstract

A new alternative technique named fifth order Improved Runge-Kutta (IRK5) method is applied to compute ahyperchaotic finance system, which needs less number of function evaluations per time step.This method obtains a solution in terms of a rapidly convergent infinite power seriescompared to fourth order RungeKutta (RK4) and fifth order Diagonally Implicit Runge-Kutta (DIRK5) methods. Moreover, the residual error of the IRK5 solution is defined and computed for each time interval. Via the computing of the residual error we observe that the accuracy of the IRK5 method compared to DIRK5.