METHODOLOGICAL INSIGHTS INTO SOLVING INITIALVALUE PROBLEMS USING DTM AND SPECIALMULTISTEP TECHNIQUES

Abstract

The paper explores the application of numerical techniques
to solve differential equations, particularly when closed-form solutions are unavailable or difficult to obtain. It focuses on methods like Differential Transform and Multistep approaches to solve differential equations with initial conditions. These techniques have significantly advanced the investigation of differential equations and are extensively used in numerous
fields such as fundamental sciences, engineering, technology and economics. Present study highlights the importance of developing more precise and efficient numerical methods, emphasizing convergence stability and in multistep approaches. The results of different techniques are compared to demonstrate their effectiveness. The paper underscores the necessity
for ongoing research to enhance numerical methods for solving differential equations, aiming for greater accuracy and efficiency in practical applications.