Dynamical analysis of a nonlinear oscillator chain in the Peyrard–Bishop DNA model using residual power series and Laplace residual power series method

In this study, we investigate the numerical exploration of the Peyrard–Bishop DNA (PBD) dynamic model. These solutions are responsible for analyzing the nonlinear interactions between the adjacent displacements of the DNA strand. To obtain these solutions, the authors present two highly effective and precise techniques for solving the nonlinear PBD dynamic model: the Residual Power Series Method (RPSM) and the Laplace Resid-ual Power Series Method (LRPSM), applied under initial and boundary conditions. The concept is explained through various numerical examples, demonstrating its practical application and ease of use. A convergence analysis has been provided between the exact and approximate solutions. These physical characteristics are thoroughly analyzed through graphical representations. The proposed methods are compared with other numer-ical techniques to showcase their applicability, accuracy, and efficiency. Two test case problems are solved, and the results are presented as tables and figures using MATHEMATICA software. The solutions illustrate the successful applications of the proposed methods, which can assist in finding numerical solutions to other nonlinear problems