Taylor Galerkin Method for Complex Differential Equations
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)
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