第一类弱奇异Volterra积分方程解的渐近展开式  

Asymptotic Expansions to the Solution of Weakly Singular Volterra Integral Equation of the First Kind

作　　者：刘思靖 王同科[1] LIU Sijing;WANG Tongke(School of Mathematical Sciences,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《应用数学》2022年第1期87-98,共12页Mathematica Applicata

基　　金：国家自然科学基金(11971241);天津市高等学校创新团队培养计划项目(TD13-5078)。

摘　　要：针对核函数和自由项代数且对数奇异的第一类线性Volterra积分方程,通过Laplace变换导出这类方程的解在零点的渐近展开式,对于方程解的奇异性质给出准确刻画.对于核函数仅代数奇异的情形,还得到方程的解在无穷远点的渐近展开式.这些展开式可以分别作为当自变量变小或变大时方程的近似解.最后,给出实例说明展开式的正确性及有效性.For the first kind linear Volterra integral equation involving algebraic and logarithmic singularities in the kernel function and free term, the asymptotic expansion for the solution about zero is derived via Laplace transform, which accurately describes the singular behavior of the solution. For the kenel function involving only algebraic singularity, the asymptotic expansion for the solution at infinty is also derived. These expansions can be used to approximate the solution when the independent variable becomes small or large, respectively. Finally, some examples are given to illustrate the correctness and effectiveness of these expansions.

关 键 词：第一类弱奇异Volterra积分方程 LAPLACE变换 解在零点的渐近展开式 解在无穷远点的渐近展开式 

分 类 号：O175.5[理学—数学] O241.83[理学—基础数学]