Approximate solution of higher-order oscillatory differential equations via modified linear block techniques

Abstract

In many areas of science and engineering, problems modeled by ordinary differential equations (ODEs) often lack analytical solutions, requiring the use of numerical methods for approximation. The proposed method tackles the challenges of solving higher-order oscillatory differential equations and introduces a new linear block technique for directly solving these equations. This method improves accuracy, reduces computational effort, and simplifies coding complexity compared to previous approaches. A generalized algorithm is presented to derive the proposed method, which enhances existing techniques for second-order and higher-order oscillatory problems. The basic properties of the method were numerically analyzed, confirming its accuracy, stability, consistency, and convergence. The proposed method proves to be efficient and suitable for various test problems, including real-life problems, which demonstrate its accuracy as compared to the existing methods.