Numerical solutions of an initial value Cauchy problem in neutrosophic environment

An initial value Cauchy problem has been considered in neutrosophic environment. The conditions for the existence and uniqueness of the solution to the neutrosophic Cauchy problem have been analysed, providing a theoretical guarantee of the well-posedness of the solution. A classical form of Euler’s method is modified and adapted to address the neutrosophic initial value problem. The conditions for the convergence of the proposed neutrosophic Euler’s method are analysed. To illustrate the theoretical findings, a numerical example is presented, demonstrating the verification of existence and uniqueness conditions, application of the modified method, and validation of the convergence criteria. Error analysis is carried out to substantiate the convergence behaviour, and the numerical results are presented through comprehensive figures and tables. This work enhances classical numerical approaches by incorporating a neutrosophic environment, offering a novel computational framework for problems involving uncertainty.