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Analytic approximate solution for Falkner-Skan equation
Vasile Marinca1, Remus-Daniel Ene2, Bogdan Marinca3
1Department of Mechanics and Vibration, Politehnica University of Timi ș oara, 300222 Timi ș oara, Romania ; Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romania Academy, 300223 Timi ș oara, Romania.
This study introduces an effective analytical method, the optimal homotopy asymptotic method (OHAM), for solving the Falkner-Skan nonlinear differential equation. OHAM offers accurate and rapidly converging solutions for boundary-layer problems without relying on small parameters.
Area of Science:
- Fluid dynamics
- Applied mathematics
- Numerical analysis
Background:
- The Falkner-Skan equation is a fundamental nonlinear differential equation arising in boundary-layer theory.
- Analytical approximate techniques are crucial for solving complex differential equations where exact solutions are difficult to obtain.
- Existing methods may depend on small parameters, limiting their applicability.
Purpose of the Study:
- To introduce and validate the optimal homotopy asymptotic method (OHAM) for solving the Falkner-Skan nonlinear differential equation.
- To demonstrate OHAM's ability to provide accurate approximate solutions for boundary-layer problems.
- To highlight OHAM's independence from small parameters and its control over solution convergence.
Main Methods:
- The optimal homotopy asymptotic method (OHAM), an analytical approximate technique.
- Application of OHAM to a boundary-layer problem governed by the Falkner-Skan equation.
- Comparison of OHAM results with established numerical solutions.
Main Results:
- OHAM provides effective, simple, and accurate analytical approximate solutions.
- The method demonstrates excellent agreement with numerical solutions.
- OHAM ensures rapid convergence, often within a single iteration, and offers optimal control over the approximation process.
Conclusions:
- The optimal homotopy asymptotic method (OHAM) is a highly effective and accurate technique for solving the Falkner-Skan nonlinear differential equation.
- OHAM's independence from small parameters and its convergence control make it a versatile tool for boundary-layer problems.
- The efficiency and accuracy of OHAM are validated by its strong agreement with numerical solutions.
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