Study of multi-dimensional problems arising in wave propagation using a hybrid scheme

Area of Science:

• Applied Mathematics
• Numerical Analysis
• Wave Propagation

Background:

• Wave propagation phenomena are fundamental in many scientific fields.
• Existing methods like VIM and HAM have limitations in developing recurrence relations.
• Efficient approximation solutions for multi-dimensional wave problems are crucial.

Purpose of the Study:

• To present an effective and suitable iterative technique for approximating solutions to multi-dimensional wave propagation problems.
• To overcome the limitations of existing methods by introducing a novel approach.
• To enhance time efficiency and reduce numerical work.

Main Methods:

• A new iterative strategy is employed.
• The Sawi integral transform is utilized to construct a suitable recurrence relation.
• This recurrence relation is solved to determine coefficients for the homotopy perturbation strategy (HPS).

Main Results:

• The proposed method provides approximation solutions in algebraic form, independent of discretization.
• It demonstrates minimum time efficiency compared to variational iteration method (VIM) and homotopy analysis method (HAM).
• Mathematical frameworks and visual depictions confirm the scheme's performance.

Conclusions:

• The Sawi integral transform combined with HPS offers an effective and efficient technique for solving wave propagation problems.
• This approach overcomes drawbacks of traditional methods, providing accurate, discretization-free solutions.
• The method shows significant improvements in efficiency and applicability for complex wave phenomena.