一类非齐次变型Bessel方程边值问题的构造解法及应用

The Constructive Solution and Application of BVP for a Class of Non-Homogeneous Bessel Equations

摘要: 本文给出了一类二阶线性常微分方程边值问题的构造解法，运用此方法进一步求得了在相同边界条件下的非齐次零阶变型Bessel方程边值问题的解，并将该理论应用于具有源汇影响的变流率平面径向渗流力学问题中，结合Laplace变换法求得了该渗流力学模型在三种外边界条件下的连分式解式。研究表明，该方法可以方便、快捷地构造出此类边界条件下的统一解式，对同类边界条件下的扩散(热传导、渗流)方程求解具有重要意义。

Abstract: This paper gives a constructive solution of a class of second order linear ordinary differential equation boundary value problem, by using this method, a non-homogeneous zero order modified Bessel equation BVP in the same boundary conditions is solved. Then the theory is also applied to the plane radial seepage mechanics with variable flow rate and source sink effect, combined with Laplace transform method, the continued fraction solutions of the seepage mechanics model under three kinds of external boundary conditions are obtained. The results show that this method can easily and quickly construct the unified solution under the same boundary conditions, which is of great significance for solving the diffusion (heat conduction, seepage) equation under the same boundary conditions.