On the application of efficient block hybrid technique in solving strongly nonlinear oscillators

Abstract

In this paper, an innovative block hybrid technique is proposed to solve strongly nonlinear oscillators. This numerical method utilizes a quasilinearization approach to linearize the nonlinear equations. The applicability and efficiency of this method is demonstrated by solving various test examples with oscillatory behavior. Theoretical analysis has been done by furnishing essential properties of the block hybrid method. The proposed method is bench-marked against the local linearization-based multi-domain spectral collocation method and ode45 MATLAB numerical solver. The results confirm that the numerical methods demonstrate good accuracy, numerical stability, and computational efficiency, with the proposed block hybrid method emerging as the most accurate, stable, and efficient iterative method that is zero-stable and converges very quickly. The enhanced accuracy is due to the incorporation of more intra-step points, resulting in higher-order truncation errors. However, superior numerical stability and computation efficiency are caused by the well-conditioned nature of the resulting coefficient matrix. In view of these advantages, the block hybrid method should be the preferred numerical method for solving strongly nonlinear equations, offering significant benefits in terms of accuracy, computational efficiency, numerical stability, and flexibility.