Taylor-Galerkin method for solving higher-order nonlinear complex differential equations
2024

Taylor Galerkin Method for Complex Differential Equations

publication Evidence: high

Author Information

Author(s): Humayun Kabir Md., Shafiqul Islam Md., Kamrujjaman Md.

Primary Institution: Bangabandhu Sheikh Mujibur Rahman University, Kishoreganj, Bangladesh

Hypothesis

The study proposes a new technique called the Taylor Galerkin Method (TGM) for solving higher-order nonlinear complex differential equations.

Conclusion

The proposed method demonstrates higher accuracy and stability compared to existing methods for solving complex differential equations.

Supporting Evidence

  • The proposed method achieves higher-order accuracy by incorporating derivatives of the solution.
  • Comparative results show that TGM outperforms existing Taylor and Bessel Collocation methods.
  • The method can be applied to a variety of spatial discretization techniques.

Takeaway

This study introduces a new way to solve tricky math problems involving complex equations, making it easier to find accurate answers.

Methodology

The study uses the Taylor Galerkin Method, which employs Taylor series expansions for discretization and error analysis.

Limitations

The method may incur additional computational costs due to the need for higher-order derivatives and complex numerical implementation.

Digital Object Identifier (DOI)

10.1016/j.mex.2024.103078

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