信阳师范学院学报（自然科学版）2025，Vol.38Issue(1)：92-100,9.DOI:10.3969/j.issn.2097-583X.2025.01.013
Sinc配点法与sinh变换求解奇异摄动过渡层问题
Sinc collocation method and sinh transform for solving singular perturbed problems with a transition layer
摘要
Abstract
High-order Sinc collocation method was used to solve a class of singular perturbed problems with a transition layer. Combined with the double exponential transform,Sinc collocation method defined naturally on the unbounded domain as available to the two-point boundary value problem with homogenous Dirichlet boundary conditions. For non-homogenous Dirichlet boundary conditions,a linear function was designed to reconstruct the unknown function. That is,it transformed the original problem into the problem with homogenous Dirichlet boundary conditions. The sinh transform was utilized to make the Sinc nodes dense in the location of the transition layer,which leaded to good accuracy with less computational cost. Based on the double exponential transform,a Sinc-barycentric form interpolation formulae defined on the bounded domain was proposed to improve the performance of the numerical approximation of non-node function values. Numerical results verified the computational efficiency of the Sinc collocation method,which combined with the double exponential transform and the sinh transform,for solving singular perturbed problems with a transition layer and the non-stationary Burgers' equation with a shock wave.关键词
过渡层/Sinc配点法/双指数变换/sinh变换/重心形式Sinc插值公式Key words
transition layer/Sinc collocation method/double exponential transform/sinh transform/Sinc-barycentric interpolation分类
数理科学引用本文复制引用
邵文婷,郑烁宇..Sinc配点法与sinh变换求解奇异摄动过渡层问题[J].信阳师范学院学报（自然科学版）,2025,38(1):92-100,9.基金项目
国家自然科学基金项目(12001362,11526132) （12001362,11526132）
上海市自然科学基金项目(16ZR1412700) （16ZR1412700）
上海市教委高校优秀青年教师专项基金项目(ZZEDG15008) （ZZEDG15008）
