Numerical Analysis of the Mixed 4th-Order Runge-Kutta Scheme of Conditional Nonlinear Optimal Perturbation Approach for the EI Niño-Southern Oscillation Model

Abstract

In this paper, we propose and analyze the mixed 4th-order Runge-Kutta scheme of conditional nonlinear perturbation (CNOP) approach for the EI Niño-Southern Oscillation (ENSO) model. This method consists of solving the ENSO model by using the mixed 4th-order Runge-Kutta method. Convergence, the local and global truncation error of this mixed 4th-order Runge-Kutta method are proved. Furthermore, optimal control problem is developed and the gradient of the cost function is determined.