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Initial value problems for system of differential-algebraic equations in Maple.

Srinivasarao Thota1

  • 1Department of Applied Mathematics,School of Applied Natural Sciences, Adama Science and Technology University, Post Box No. 1888, Adama, Ethiopia. srinithota@ymail.com.

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Summary
This summary is machine-generated.

This study introduces deaSolve, a Maple package for solving linear differential-algebraic equations. It enables symbolic computation of Green's functions for initial value problems.

Keywords:
Differential-algebraic systemsGreen’s functionInitial value problemsMaple packagesSymbolic algorithm

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Area of Science:

  • Numerical Analysis
  • Symbolic Computation
  • Differential Equations

Background:

  • Solving systems of linear differential-algebraic equations (DAEs) is crucial in various scientific and engineering fields.
  • Existing methods may lack efficiency or symbolic manipulation capabilities for complex problems.
  • Initial value problems (IVPs) for DAEs present unique challenges in finding analytical solutions.

Purpose of the Study:

  • To present a novel Maple package, deaSolve, designed for the symbolic solution of IVPs for linear DAEs with constant coefficients.
  • To provide a user-friendly tool for researchers and practitioners working with such equations.
  • To facilitate the computation of Green's functions for DAE systems.

Main Methods:

  • Development of a symbolic algorithm implemented within a Maple package named deaSolve.
  • Focus on systems of linear differential-algebraic equations with constant coefficients.
  • Utilizing symbolic computation techniques for analytical solution derivation.

Main Results:

  • The deaSolve package successfully implements the symbolic algorithm for solving the specified IVPs.
  • The package allows for the direct computation of the Green's function associated with a given IVP.
  • Illustrative sample computations demonstrate the package's functionality and effectiveness.

Conclusions:

  • The deaSolve Maple package offers an efficient symbolic approach for solving IVPs of linear DAEs.
  • The ability to compute Green's functions enhances the utility of the package for analysis and simulation.
  • This tool provides a valuable resource for the symbolic solution of differential-algebraic equations.