Numerical Solutions of Higher Order Differential Equations via New Iterative Method.

Abstract

Higher order differential equations play a fundamental role in various scientific and engineering disciplines, but their numerical solutions often pose formidable challenges. The New Iterative Method (NIM) has emerged as a promising technique for addressing these challenges. This study is to explore and assess the efficiency and accuracy of New Iterative Method in solving higher-order differential equations. By applying NIM to a range of problems from diverse scientific disciplines, we aim to provide insights into the method's adaptability and its potential to revolutionize numerical analysis. The method is well-suited for numerically integrating both and nonlinear higher-order differential equations. To showcase the efficiency and accuracy of this approach, some numerical tests have been conducted, comparing it to existing methods. The numerical results obtained from these tests strongly suggest that the new iterative scheme outperforms the previously employed method in estimating higher-order problems, thus confirming its convergence.