A uniqueness theorem for a boundary value problem
A uniqueness theorem for a boundary value problem
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DOI：
10.1090/s0002-9939-1979-0545591-4
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发表时间：
1979-03
期刊：
影响因子：
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通讯作者：
R. Usmani
中科院分区：
文献类型：
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作者：
R. Usmani
本文证明了两点边值问题，即(d(4)/dx4 + fy = g, y(O) A1 = y(l) A2 = Y"(O)BI = y"(l) B2 = 0，有唯一解，条件为fxf(x) = i > V4。给定的边值问题通过有限差分格式离散化。该数值逼近被证明是一个二阶收敛过程： 使用向量的 L2 范数建立误差界限。
In this paper it is proved that the two-point boundary value problem, namely (d(4)/dx4 + fy = g, y(O) A1 = y(l) A2 = Y"(O)BI = y"(l) B2 = 0, has a unique solution provided infxf(x) = i > V4. The given boundary value problem is discretized by a finite difference scheme. This numerical approximation is proved to be a second order convergent process by establishing an error bound using the L2-norm of a vector.