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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (1): 147-158.doi: 10.3969/j.issn.1005-3085.2023.01.011

• • 上一篇    下一篇

带化学反应的边界层流动问题中一类弱奇异 Volterra 积分方程的近似解

季  鹭1,   王同科1,   高广花2   

  1. 1. 天津师范大学数学科学学院，天津 300387；2. 南京邮电大学理学院，南京 210023
  • 出版日期:2023-02-15 发布日期:2023-04-11
  • 通讯作者: 王同科 E-mail: wangtke@sina.com
  • 基金资助:
    国家自然科学基金(11971241)；江苏省自然科学基金(BK20191375)；天津市高等学校创新团队培养计划(TD13-5078).

The Approximate Solutions to a Class of Weakly Singular Volterra Integral Equations in the Problem of Boundary Layer Flow with Chemical Reaction

JI Lu1,   WANG Tongke1,   GAO Guanghua2   

  1. 1. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387;
    2. College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023
  • Online:2023-02-15 Published:2023-04-11
  • Contact: T. Wang. E-mail address: wangtke@sina.com
  • Supported by:
    The National Natural Science Foundation of China (11971241); the Natural Science Foundation of Jiangsu Province (BK20191375); the Program for Innovative Research Team in Universities of Tianjin (TD13-5078).

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摘要：

研究带化学表面反应的边界层流动问题导出的一类弱奇异Volterra积分方程的近似解。以一些化学反应的阶数为例求出解在零点的分数阶级数展开式及其Pad$\acute{\rm e}$有理逼近。通过将发散积分解释为Hadamard有限部分积分，并借助数值积分方法导出解在无穷远点的带高阶对数项的渐近展开式。实际计算表明，给出的解在零点和无穷远点展开式的联合使用可以在整个半无限区间上高效地求解这类带化学表面反应的边界层流动问题。

关键词: 边界层流动, 化学表面反应, 弱奇异Volterra积分方程, Hadamard有限部分积分, 解在零点的展开式, 解在无穷远点的展开式

Abstract:

The approximate solutions are established for a class of weakly singular Volterra integral equations derived from the boundary layer flow with a chemical surface reaction. Taking some orders of chemical reaction as examples, the fractional series expansions about zero and their Pad$\acute{\rm e}$ rational approximations are obtained. By interpreting the divergent integrals as the Hadamard finite part integrals, the asymptotic expansions with higher order logarithmic terms at infinity are derived with the aid of the numerical integration method. Practical calculation shows that the combination of the expansions at zero and infinity can efficiently solve this kind of boundary layer flow problem with chemical surface reaction on the whole half infinity interval.

Key words: boundary layer flow, chemical surface reaction, weakly singular Volterra integral equation, Hadamard finite part integral, expansion of solution about zero, expansion of solution at infinity

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