Mathematical Sciences: Error Bounds for Uniform Asymptotic Approximations

这项工作涉及到错误约束理论的构建 一些重要的和长期存在的问题， 渐近分析 将尝试得出现实的 定常微分方程一致渐近展开式的误差界 积分与凝聚鞍点，并为均匀 带两个变量的非线性方程的渐近展开式 在复平面中合并转折点。 的作用 渐近展开式中的指数小项将是 考察 简化一些现有的 扩展，以便它们可以更容易地在复杂的 飞机也将被考虑。 这项工作应该是非常有价值的研究人员在 物理学、生物学和工程学， 模型方程，适当的缩放，涉及大或小 参数

This work involves the construction of error-bound theories for a number of important and long-standing problems in asymptotic analysis. Attempts will be made to derive realistic error bounds for uniform asymptotic expansions of definite integrals with coalescing saddle points, and for uniform asymptotic expansions of differerential equations with two coalescing turning points in the complex plane. The role of exponentially small terms in asymptotic expansions will be examined. The possibility of simplifying some existing expansions so they may be more readily computed in the complex plane will also be considered. This work should be of great value to researchers in the physical, biological, and engineering sciences where many of the model equations, with proper scaling, involve large or small parameters.