Solving a class of ODEs arising in the analysis of a computer security process using generalized hyper-Lambert functions

International Journal of Applied Mathematics and Computation

Yiannis C. Stamatiou¹  Apostolos Tsiakalos¹  Panayotis E. Nastou² 

[1] Department of MathematicsUniversity of Ioannina$$;Department of MathematicsUniversity of the AegeanKarlovasi, Samos, Greece$$

关键词: ODEs;    Lambert W function;    Generalized Hyper-Lambert functions;    Key Agreement;   

DOI  :  10.0000/ijamc.2012.4.3.474

来源: PSIT Kanpur

【 摘 要 】

In this paper, we derive the solution to a class of ordinary differential equations (ODEs) that arise from the theoretical analysis, conducted in a previous work, of a key agreement process stemming from computer security. The analysis led to a new class of ordinary differential equations that resemble the well known class of Abel differential equations of the First Kind except that this new class involves the unknown function in powers greater than three. To the best of our knowledge, no general solution strategy exists for integrating the differential equations in this class towards a solution. We show that the solution to these ordinary differential equations can be expressed, interestingly, through the use of a class of Generalized Hyper-Lambert Functions that naturally generalize the well known Lambert $W$ function, which frequently arises in the analysis of engineering applications. A key step to the connection of the solution of the differential equations with Generalized Hyper-Lambert Functions is the analysis of the equations into partial fractions in a way that matches the recursive pattern of the definition of these functions.

【 授权许可】

Unknown