CAJ | 학술논문

针对Airy方程的一类边值问题,经变量替换将其转换成变型的Bessel方程的边值问题,通过研究解式的相似结构,得到了相似核函数;经分析,此边值问题可以先由Airy方程的任意两个线性无关的解和右边界条件系数构造出相似核函数,再由左边界条件中的系数决定的相似结构式进行组装,得到Airy方程的一类边值问题的解,从而获得求解该类边值问题的一个新方法———相似构造法;该方法对进一步的分析解的内在规律及编制相应的分析软件提供了新思路.
침대Airy방정적일류변치문제,경변량체환장기전환성변형적Bessel방정적변치문제,통과연구해식적상사결구,득도료상사핵함수;경분석,차변치문제가이선유Airy방정적임의량개선성무관적해화우변계조건계수구조출상사핵함수,재유좌변계조건중적계수결정적상사결구식진행조장,득도Airy방정적일류변치문제적해,종이획득구해해류변치문제적일개신방법———상사구조법;해방법대진일보적분석해적내재규률급편제상응적분석연건제공료신사로.
Variable substitution are used in this paper to translate a kind of boundary -value problem of Airy equations into modified Bessel equations , and the similar kernel function is obtained through the analysis of the similar structure of solution . Solution of the equation boundary -value problem is acquired by structuring Similarity kernel function with any two linearly in-dependence solutions of Airy equation and coefficients of right boundary condition first , and then assembling with the similar structure determined by the coefficients of left boundary condition , thus similarity construction method , a new method of sol-ving this kind of boundary -value problem, is obtained;This method open a new way to analysis solution of the inherent law and design relevant analysis software .