A numerical solution of a singular boundary value problem arising in boundary layer theory

Area of Science:

• Numerical Analysis
• Computational Fluid Dynamics
• Applied Mathematics

Background:

• Singular boundary value problems (BVPs) are common in various scientific fields.
• The Falkner-Skan equation is a well-known example of such problems, often encountered in fluid dynamics.
• Existing numerical methods can be computationally intensive.

Purpose of the Study:

• To introduce a novel finite difference method for solving a specific second-order nonlinear singular BVP.
• To demonstrate the equivalence between a third-order BVP and a second-order BVP.
• To provide a computationally efficient alternative to existing numerical techniques.

Main Methods:

• Transformation of a one-dimensional third-order BVP into a second-order BVP on a finite interval.
• Application of the finite difference method to discretize and solve the resulting second-order singular BVP.
• Comparison of computational effort with other numerical methods.

Main Results:

• The proposed finite difference method effectively solves the singular boundary value problem.
• The method demonstrates significantly reduced computational effort compared to other numerical approaches.
• Numerical solutions obtained align well with results from previous studies.

Conclusions:

• The finite difference method is a viable and efficient technique for solving this class of singular BVPs.
• This approach offers a computationally advantageous alternative for problems related to the Falkner-Skan equation.
• The study validates the accuracy and efficiency of the proposed numerical scheme.