Extending high order derivatives for special differential equations of the form \(y' = f(y)\) by using monotonically labeled rooted trees.
2015 ◽
Vol 4
(4)
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pp. 513
Keyword(s):
<p>This paper presents a review of the role played by labeled rooted trees to obtain derivatives for numerical solution of initial value problems in special case \(y' = f(y), y(x_0) = y_0\). We extend a process to find successive derivatives according to monotonically labeled rooted trees, and prove some relevant lemmas and theorems. In this regard, the derivatives, of the monotonically labeled rooted trees with n vertices are presented by using the monotonically labeled rooted trees with k + n vertices. Eventually, this process is applied to trees without labeling.</p>
1979 ◽
Vol 33
(145)
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pp. 111-124
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2001 ◽
Vol 77
(3)
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pp. 457-467
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1981 ◽
Vol 7
(2)
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pp. 111-114
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1957 ◽
Vol 10
(2)
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pp. 232-243
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2020 ◽
Vol 148
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pp. 140-151
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1975 ◽
pp. 197-211
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