We propose a uniformly convergent numerical scheme for singularly perturbed boundary value problems with a single boundary layer. The method combines the advantages of reproducing kernel theory with a domain decomposition strategy. Without loss of generality, we focus on problems exhibiting a left boundary layer, as the analysis for a right layer is mathematically equivalent. The original problem is first split into a boundary layer problem and a regular problem. The regular part is solved numerically using a high-order reproducing kernel collocation method on a uniform mesh, while the boundary layer part is resolved on a graded mesh using a similar high-order scheme. Both theoretical analysis and numerical experiments confirm the parameter-uniform convergence of the proposed approach.
Li, X. L. and Geng, F. (2026). Solve linear singularly perturbed boundary value problems via domain decomposition and reproducing kernel collocation. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.70289.3481
MLA
Li, X. L. , and Geng, F. . "Solve linear singularly perturbed boundary value problems via domain decomposition and reproducing kernel collocation", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.70289.3481
HARVARD
Li, X. L., Geng, F. (2026). 'Solve linear singularly perturbed boundary value problems via domain decomposition and reproducing kernel collocation', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.70289.3481
CHICAGO
X. L. Li and F. Geng, "Solve linear singularly perturbed boundary value problems via domain decomposition and reproducing kernel collocation," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.70289.3481
VANCOUVER
Li, X. L., Geng, F. Solve linear singularly perturbed boundary value problems via domain decomposition and reproducing kernel collocation. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.70289.3481
)