A Novel Numerical Technique for Solving Singularly Perturbed Differential Equations With Mixed Boundary Conditions

Key Points

• To develop and analyze a new numerical technique for solving singularly perturbed differential equations with mixed boundary conditions.
• Determination of boundary values and their derivatives.
• Construction of a difference scheme on the Shishkin mesh.
• Analysis of uniform convergence and stability with a perturbation parameter.
• Testing and discussing convergence and stability of the numerical technique.
• The numerical technique demonstrates theoretical convergence and stability.
• Numerical results confirm the effectiveness of the proposed method.

Abstract