A comparative analysis for the solution of nonlinear Burgers' equation

Area of Science:

• Applied Mathematics
• Numerical Analysis
• Partial Differential Equations

Background:

• Coupled Burgers' equations model complex phenomena like fluid dynamics and traffic flow.
• Accurate and efficient numerical methods are crucial for analyzing these equations.
• Several analytical and numerical techniques exist, but their comparative performance is not well-established.

Purpose of the Study:

• To conduct a comparative analysis of seven prominent mathematical techniques for solving coupled Burgers' equations.
• To evaluate the convergence and stability of each method.
• To identify the most effective technique for practical applications.

Main Methods:

• Laplace transform Adomian decomposition method
• Laplace transform homotopy perturbation method
• Variational iteration method
• Variational iteration decomposition method
• Variational iteration homotopy perturbation method
• Optimal homotopy asymptotic method (OHAM)
• OHAM with Daftardar-Jafari polynomial

Main Results:

• The variational iteration method demonstrated superior convergence rates compared to other techniques.
• The Adomian decomposition method and homotopy perturbation method exhibited lower stability.
• All methods were applied to a specific case of coupled Burgers' equations with kinematic viscosity ε=1.

Conclusions:

• The variational iteration method is recommended for its faster convergence in solving coupled Burgers' equations.
• Careful selection of numerical techniques is essential for stability and efficiency.
• This comparative study provides valuable insights for researchers working with coupled Burgers' equations.