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On solving system of differential-algebraic equations using adomian decomposition method.

Srinivasarao Thota1, Shanmugasundaram P2

  • 1Department of Mathematics, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, 522503, India.

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Summary

This study introduces an efficient Adomian decomposition method (ADM) for solving second-order nonlinear differential-algebraic equations (DAEs). The ADM provides rapid, approximate solutions applicable to various real-world problems.

Keywords:
Adomian decomposition methodApproximate solutions.Differential-algebraic equations

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Area of Science:

  • Numerical Analysis
  • Applied Mathematics
  • Computational Science

Background:

  • Focuses on solving systems of second-order nonlinear differential-algebraic equations (DAEs).
  • Addresses the need for efficient and straightforward solution methodologies.

Purpose of the Study:

  • To present an efficient and easy semi-analytical method for solving second-order nonlinear DAEs.
  • To demonstrate the applicability and effectiveness of the Adomian decomposition method (ADM).

Main Methods:

  • Employs the Adomian decomposition method (ADM), a semi-analytical technique.
  • The method is characterized by its simplicity and straightforward implementation.

Main Results:

  • Approximate solutions for systems of second-order nonlinear DAEs are computed rapidly and efficiently.
  • Demonstrated efficiency through several examples, comparing computations with exact solutions.
  • The method's logic is adaptable to various mathematical software tools like MATLAB and Mathematica.

Conclusions:

  • The Adomian decomposition method (ADM) is presented as a simple and efficient approach for solving second-order nonlinear DAEs.
  • The method allows for quick acquisition of approximate solutions.
  • Illustrative examples and assessments confirm the method's validity and practical utility.