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Objective <p>The vibration equation of a very large membrane is investigated using a new approach, namely the Yang Projected Differential Transform Method (YPDTM), to obtain explicit solutions.</p> Methodology <p>The proposed methodology integrates Yang’s transformation with the projected differential transform technique while systematically incorporating the prescribed initial conditions.</p> Result <p>By applying this&#xa0;unified framework, rapidly convergent series solutions are derived for various cases corresponding to different initial conditions. The accuracy and reliability of the obtained results are validated through appropriate comparisons with existing methods.</p> Conclusion <p>Furthermore, graphical illustrations are provided to demonstrate the effectiveness and study the behaviour of the solution obtained by the proposed approach.</p>

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A Numerical Solution to the Vibration Equation of Large Membrane Using Yang Projected Differential Transform Method

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Diptiranjan Behera

摘要

Objective

The vibration equation of a very large membrane is investigated using a new approach, namely the Yang Projected Differential Transform Method (YPDTM), to obtain explicit solutions.

Methodology

The proposed methodology integrates Yang’s transformation with the projected differential transform technique while systematically incorporating the prescribed initial conditions.

Result

By applying this unified framework, rapidly convergent series solutions are derived for various cases corresponding to different initial conditions. The accuracy and reliability of the obtained results are validated through appropriate comparisons with existing methods.

Conclusion

Furthermore, graphical illustrations are provided to demonstrate the effectiveness and study the behaviour of the solution obtained by the proposed approach.