Numerical solution of functional differential equations using legendre wavelet method

In this paper, the objective is to solve the functional differential equations in the following form using Legendre Wavelet Method (LWM), where f: [t ₀, t/]xR ²→R is a smooth function, α(t) is a continuous function on [t ₀, t _f] and φ(t)∈C represents the initial point or the initial data. In the present paper, the most important advantages of using of the proposed method are illustrated. Some experiments are employed to illustrate the validity and flexibility of LWM, in particular for nonlinear functional differential equations.