Department of Applied Mathematics, Vidyasagar University, Midnapore-721102, India
In the realm of neutrosophic mathematics, solving differential equations introduces complexities due to the uncertain nature of the parameters involved. This study explores the application of Milne's predictor and corrector formula within the neutrosophic environment to solve ordinary differential equations (ODEs) with initial conditions. The approach leverages the flexibility of neutrosophic sets to represent vague or imprecise initial conditions and parameters. Milne's method, known for its efficiency in predicting and correcting numerical solutions, is adapted to accommodate neutrosophic uncertainties, enhancing its applicability in practical scenarios where precise initial conditions may be lacking. Through theoretical analysis and computational experiments, this research demonstrates the effectiveness of combining neutrosophic calculus with Milne's formula, offering insights into its potential for solving ODEs under uncertain conditions.
Fuzzy number, Neutrosophic number, Neutrosophic function, Neutrosophic ODE
