Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions

Abstract

The ordinary differential equation of second order is being used in many engineering
disciplines and sciences to model many real-life problems. These problems are mostly uncertain,
vague and incomplete and thus they require some more advanced tool for modelling.
Neutrosophic logic becomes the solution of all these kind of uncertain problems as it describe the
conditions of uncertainty which occurs during the process of modelling on the basis of grade of
membership of truth values, indeterminacy values and falsity values, that means it consider all the
uncertain parameters on the basis of these degrees. In this research paper, we have considered the
ordinary differential equation of second order with neutrosophic numbers as initial conditions of
spring mass system is solved using Sumudu transform method which has advantage of unit
preserving property over the well established Laplace Transform method. The solution obtained at
various computational points by this method is shown in the form of table. Furthermore, the results
obtained at different (α, β, γ)-cut and time values are also depicted graphically and are verified
analytically by de-fuzzifying the data.