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On solving initial value problems for partial differential equations in maple.

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  • 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 a symbolic Maple software algorithm for solving initial value problems (IVPs) of partial differential equations (PDEs). The algorithm efficiently computes operators, Green's functions, and exact solutions for applied science and engineering problems.

Keywords:
Initial value problemsMaple implementationPartial differential equationsSymbolic algorithm

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Area of Science:

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Background:

  • Partial differential equations (PDEs) are fundamental in modeling complex phenomena across sciences and engineering.
  • Solving PDEs, especially initial value problems (IVPs), often requires sophisticated computational methods.
  • Existing analytical and numerical techniques may have limitations in terms of efficiency and scope.

Purpose of the Study:

  • To present and implement a novel symbolic algorithm using Maple software for solving IVPs of PDEs.
  • To demonstrate the algorithm's capability in handling PDEs relevant to applied sciences and engineering.
  • To provide a computational tool for researchers and practitioners.

Main Methods:

  • Development of a symbolic algorithm in Maple for solving PDEs.
  • Implementation of functions for computing partial differential operators, Green's functions, and exact solutions.
  • Creation of a verification syntax (ApplyPartialDiffOp) to validate obtained solutions.

Main Results:

  • The Maple algorithm successfully computes key components for solving IVPs of PDEs.
  • The implementation includes functionalities for operator computation, Green's function derivation, and exact solution determination.
  • A verification method is provided to confirm the accuracy of the computed exact solutions.

Conclusions:

  • The presented symbolic Maple algorithm offers a significant advancement in solving IVPs of PDEs.
  • The implemented approach is effective for PDEs arising in applied sciences and engineering.
  • The software provides a practical tool for obtaining and verifying exact solutions to complex differential equations.