PERFORMANCE ASSESSMENT OF DIFFERENTIAL TRANSFORMATION AND SPECIAL MULTISTEP TECHNIQUES FOR HIGHER-ORDER DIFFERENTIAL EQUATIONS

Abstract

This research presents an approach for solving 4^th order ordinary differential equations with initial value conditions using the Differential Transformation Method (DTM) and a special multistep ND Method. Many real-world processes can be described through ordinary differential equations that represent the rate of change of physical quantities in applied mathematics, science and engineering. The DTM transforms the given problem into a system of recursive relations, leading to a power series form of the solution, while the multistep method generates numerical approximations using previously calculated values. A set of illustrative problems is considered to evaluate the performance of both techniques. The obtained results are in good agreement with the exact solutions, which helps to assess accuracy and convergence and the multistep method exhibits good numerical stability, whereas DTM offers a simple analytical framework.