Extending high order derivatives for special differential equations of the form \(y' = f(y)\) by using monotonically labeled rooted trees.
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2015-10-07 https://doi.org/10.14419/ijamr.v4i4.4691
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Labeled rooted trees, Monotonically labeled trees, Elementary differentials, Initial value problems, Derivatives. -
Abstract
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.
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References
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How to Cite
Hassani, H., & Dahaghin, M. S. (2015). Extending high order derivatives for special differential equations of the form \(y’ = f(y)\) by using monotonically labeled rooted trees. International Journal of Applied Mathematical Research, 4(4), 513-518. https://doi.org/10.14419/ijamr.v4i4.4691Received date: 2015-04-29
Accepted date: 2015-09-14
Published date: 2015-10-07