Solution and Analysis of System of Differential Equation with Initial Condition as ð“ð«ðšð©ðð§ð®ð¦ð›ðž

Abstract

In this present study, we have analyzed the solution of system of first
order simultaneous differential equations with initial condition as a neutrosophic
environment. Here, we consider the initial values as Trapezoidal Neutrosophic
Numbers (ð‘‡ð‘Ÿð‘Žð‘ð‘ð‘›ð‘¢ð‘šð‘ð‘’ð‘Ÿ). The solution procedure of the system of first order ODE
is developed using ð‘‡ð‘Ÿð‘Žð‘ð‘ð‘›ð‘¢ð‘šð‘ð‘’ð‘Ÿ and (ð›¼, ð›½, ð›¾)ð‘ð‘¢ð‘¡ of a ð‘‡ð‘ð‘›ð‘¢ð‘šð‘ð‘’ð‘Ÿ. Furthermore, a
numerical example is illustrated to validate the efficiency and feasibility of the
proposed neutrosophic method, and the solutions are compared with the crisp values.
The numerical solutions ð‘¥1
(ð‘¡, ð›¼), ð‘¥2
(ð‘¡, ð›¼), ð‘¥1
′
(ð‘¡, ð›½), ð‘¥2
′
(ð‘¡, ð›½), ð‘¥1
′′(ð‘¡, ð›¾), ð‘¥2
′′(ð‘¡, ð›¾), ð‘¦1
(ð‘¡, ð›¼),
ð‘¦2
(ð‘¡, ð›¼), ð‘¦1
′
(ð‘¡, ð›½), ð‘¦2
′
(ð‘¦, ð›½), ð‘¦1
′′(ð‘¡, ð›¾) ð‘Žð‘›ð‘‘ ð‘¦2
′′(ð‘¡, ð›¾) for the different values of ð›¼, 𛽠and ð›¾
at ð‘¡ = 0.5 are examined via tables and graphs. The numerical solutions delight the
conditions of strong solution.