Modified Numerical and Exact Solutions of Fuzzy Wave Equation under Neutrosophic Environment

In this paper, a comprehensive study of the fuzzification and defuzzification of wave equation in neutrosophic fuzzy environment is presented for first time in literature including Truth (T), Indeterminacy (I), and Falsehood (F) fuzzy component. Moreover, a numerical and analytical methods that are explicit finite difference method and D'Alembert's method are reformulate, developed, and applied for solving the neutrosophic fuzzy wave equation. The neutrosophic triangular number concept was utilized for both neutrosophic numerical and exact solutions. The error bound between the neutrosophic numerical and exact solution evaluated at (?,?,?)-cut level set is illustrated and evaluated. Finally, a numerical example is carried out and solved using both analytical and numerical techniques and the results indicate the effectiveness and feasibility of the proposed developed methods.