An efficient numerical technique for a specific family of singularly perturbed boundary value problems

This paper deals with a particular family of singularly perturbed two-point boundary value problems characterized by the perturbation parameter ۰<\varepsilon\ll ۱, and it introduces a new numerical technique to approximate its solution. As the perturbation parameter \varepsilon decreases, the majority of classic numerical methods that utilize uniform grids necessitate significantly reduced step sizes. Consequently, we employ a non-equidistant mesh. After discretizing the problem and constructed some high order compact methods, the original problem is transformed into a linear algebraic system. Also, it is demonstrated that the present method converges with order ۴ in L_\infty norm. Finally, numerical simulations will demonstrate the efficacy of the proposed method and confirm the theoretical results.

کلیدواژه ها:

Two-point boundary value problems ، perturbation parameter ، differential equation ، fourth-order convergence