二阶椭圆型方程边值问题的小波逼近

THE WAVELET APPROXIMATION TO THE BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ELLIPTIC EQUATION

二阶椭圆型方程边值问题的小波逼近朱同林华南农业大学理学院基础部，５１０６４２，广州关键词椭圆边值问题，Ｐｏｉｓｓｏｎ积分，周期小波分类号（中图）Ｏ１７５；（１９９１ＭＲ）３５Ｊ，４５Ｌ对于典型椭圆边值问题（２＋ｐ（｜Ｘ｜２））ｕ（Ｘ）＝０，Ｘ∈Ω，...

The wavelet approximation to the boundary value problems for second order elliptic equations by means of periodic Daubechies compactly supported wavelet.Firstly, the boundary value problem is reduced into a singular integral equation on boundary and is proved that its kernel is weak singular. Then the wavelet coefficients is used to turn the problem of solving the integral equation into the problem of solving a system of linear algebraic equations. In this way, the approximate solution of the boundary value problem has been obtained.And such sequence of numberial approximate solution converges to the exact solution has been proved.