BOUNDARY INTEGRAL EQUATION METHODS FOR SOLVING LAPLACE'S EQUATION WITH NONLINEAR BOUNDARY CONDITIONS: THE SMOOTH BOUNDARY CASE
BOUNDARY INTEGRAL EQUATION METHODS FOR SOLVING LAPLACE'S EQUATION WITH NONLINEAR BOUNDARY CONDITIONS: THE SMOOTH BOUNDARY CASE
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DOI：
10.1090/s0025-5718-1990-1035924-x
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发表时间：
1990-01
影响因子：
2
通讯作者：
K. Atkinson;G. Chandler
中科院分区：
文献类型：
--
作者：
K. Atkinson;G. Chandler
通过使用重构形式作为非线性边界积分方程，对拉普拉斯方程的非线性边值问题进行数值求解。提出并分析了两种离散积分方程的数值方法，两者都使用乘积积分来近似方程中的奇异积分。第一种方法使用乘积辛普森法则，第二种方法基于三角插值。还广泛讨论了求解非线性系统的迭代方法（包括两网格方法）。包括数值示例。
A nonlinear boundary value problem for Laplace's equation is solved numerically by using a reformulation as a nonlinear boundary integral equation. Two numerical methods are proposed and analyzed for discretizing the integral equation, both using product integration to approximate the singu- lar integrals in the equation. The first method uses the product Simpson's rule, and the second is based on trigonometric interpolation. Iterative methods (in- cluding two-grid methods) for solving the resulting nonlinear systems are also discussed extensively. Numerical examples are included.