Solving Lorenz System by Using Lower Order Symmetrized Runge-Kutta Methods

Runge-Kutta is a widely used numerical method for solving the non-linear Lorenz system. This study focuses on equations with classical parameter values by using lower order symmetrized methods, Implicit Midpoint Rule (IMR), and Trapezoidal (ITR). We show construction of symmetrical present experiments based two methods without symmetrization, one- two-step active symmetrization in constant step size setting. For our experiments, we use MATLAB software to solve plot graphical solutions compare oscillatory behaviour it appears that IMR turn out be chaotic while rest non-chaotic. also accuracy efficiency result shows performs better than symmetrizers, ITR one-step ITR. Based results, conclude different implicit steps can significantly impact Since most system explicit time schemes, hope this motivate other researchers analyze further schemes.