Abstract
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
Highlights
The theory of entropy was originally related with thermodynamics, but in recent years it has been used in other areas of investigation such as information theory, psychodynamics, thermoeconomics, human relationships and many more
Standard analytical schemes requisite more computer memory and computational time, to overcome these limitations the analytical methods need to be merged with standard integral transform operators to study the nonlinear equations appearing in science and engineering [24,25,26].The key purpose of the present work is to propose a novel numerical approach namely q-homotopy analysis Sumudu transform method (q-HASTM) to solve the nonlinear fractional dynamical model of interpersonal and romantic relations in marriages
We find the solution of nonlinear fractional dynamical model of interpersonal and romantic relationship written in the following form: (
Summary
The theory of entropy was originally related with thermodynamics, but in recent years it has been used in other areas of investigation such as information theory, psychodynamics, thermoeconomics, human relationships and many more. In view of the great importance of fractional approaches in real world problems we were motivated to study the nonlinear dynamical model of interpersonal and romantic relationships. Standard analytical schemes requisite more computer memory and computational time, to overcome these limitations the analytical methods need to be merged with standard integral transform operators to study the nonlinear equations appearing in science and engineering [24,25,26].The key purpose of the present work is to propose a novel numerical approach namely q-homotopy analysis Sumudu transform method (q-HASTM) to solve the nonlinear fractional dynamical model of interpersonal and romantic relations in marriages.
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