Approximate Analytical Solutions to Jerk Equations

Marinca, Vasile; Herişanu, Nicolae; Marinca, Bogdan

doi:10.1007/978-3-030-75653-6_8

Search citation statements

Order By: Relevance

Paper Sections

Select...

Approximate Analytic Solutions Via Oafm1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We introduce the basic ideas of the OAFM by considering Equation ( 5) with the initial conditions given by Equation ( 6) in general form as in [43,54]:…”

Section: Approximate Analytic Solutions Via Oafmmentioning

confidence: 99%

Approximate Closed-Form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method

2022

View full text Add to dashboard Cite

Based on some geometrical properties (symmetries and global analytic first integrals) of the Rabinovich system the closed-form solutions of the equations have been established. The chaotic behaviors are excepted. Moreover, the Rabinovich system is reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions are built using the Optimal Auxiliary Functions Method (OAFM). The advantage of this method is to obtain accurate solutions for special cases, with only an analytic first integral. An important output is the existence of complex eigenvalues, depending on the initial conditions and physical parameters of the system. This approach was not still analytically emphasized from our knowledge. A good agreement between the analytical and corresponding numerical results has been performed. The accuracy of the obtained results emphasizes that this procedure could be successfully applied to more dynamic systems with these geometrical properties.

show abstract

“…We introduce the basic ideas of the OAFM by considering Equation ( 5) with the initial conditions given by Equation ( 6) in general form as in [43,54]:…”

Section: Approximate Analytic Solutions Via Oafmmentioning

confidence: 99%