CAJ | 학술논문

将基本解方法推广到二阶和四阶椭圆型偏微分方程的对称问题，在边界上不需要处理奇异积分．通过坐标变换，将一般二阶和四阶椭圆型偏微分方程化为目前研究较为成熟的调和或双调和方程．再根据镜像法构造出适合对称条件的基本解函数，简化了计算，且不影响计算的精度，通过数值计算结果可以看出，利用镜像技术构造出的基本解，前期准备数据少，可保持精度，是一种有效的数值方法。
장기본해방법추엄도이계화사계타원형편미분방정적대칭문제，재변계상불수요처리기이적분．통과좌표변환，장일반이계화사계타원형편미분방정화위목전연구교위성숙적조화혹쌍조화방정．재근거경상법구조출괄합대칭조건적기본해함수，간화료계산，차불영향계산적정도，통과수치계산결과가이간출，이용경상기술구조출적기본해，전기준비수거소，가보지정도，시일충유효적수치방법。
Abstract The method of tile fundamental solution with image technique is used to study the partial differential equations （PDEs） of the second and forth order in this paper. This method has the merit that it does not need to deal with singular integrals on the boundaries. The PDEs are converted to the harmonic and biharmonic equations with the help of the coordinate transformation. Then, the fundamental solutions used in the calculations are built for the symmetric problemsby the image technique to simplify the computation without loss of accuracy. It is concluded from the numerical example that the relatively higher accuracy can be achieved with less data preparing by this method.