A fourth-order compact finite difference method for higher-order Lidstone boundary value problems

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• 作者：Yuan-Ming Wang ; Hai-Yun Jiang ; Ravi P. Agarwal
• 关键词：none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4RWBCXK-3&_mathId=mml32&_user=1067359&_cdi=5620&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=fa50e3196d69fa8ca893cb3f687a141b" t
• 刊名：Computers and Mathematics with Applications
• 出版年：2008
• 期刊代码：37_08981221
• 类别：cp
• 出版时间：July 2008
• 卷：56
• 期：2
• 页码：499-521
• 文件大小：623 K

摘要

While the reactions at high pH are due to

The overall rate expression over the entire pH range can be determined from (H₂A = H₂CrO₄) where k_H2A-Fe = 5 × 10⁶, k_HA-FeOH = 1 × 10⁶, k_{HA-Fe (OH)2} = 5 × 10¹¹. In oxic aqueous systems Cr(VI) competes with O₂ in the oxidation of Fe(II) and an extension of the rate law for Cr(VI) reduction with Fe(II) in oxygenated solutions is proposed. The application of this extended rate law to environmental conditions suggests that this reaction influences the distribution of oxidized and reduced species of chromium in oxic and anoxic waters.