On the Equivalence of the Differential Transform Method and the Elzaki Transform Method for Nonlinear Initial Value Problems
Abstract
In this paper, we examine two semi-analytical techniques, the Differential Transform Method and the Elzaki Transform Method for solving nonlinear ordinary differential equations . These methods were illustrated on two different nonlinear differential equations with initial values. The series solutions using both methods were computed and the solutions compared with the exact solutions. The results show that the Differential Transform Method and the Elzaki Transform Method both reproduce the truncated Taylor expansion of the exact solutions for the two problems. Numerical results show perfect agreement between DTM and ETM, confirming their equivalence for nonlinear initial value problems. Therefore, both methods can be used effectively.
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