Numerical and theoretical analysis for fixed points for solving differential equation with retarded argument using an efficient iterative method

A. Mushtaq, K. Moinuddin, N. Sharma, V. N. Mishra

This paper includes a new three stage iterative method AM^* and uses that method to test some convergence theorems in Banach spaces, together with the example to prove efficiency of AM^* is the central focus of this paper, along with explaining, using an example, that AM^* is converging to an invariant point faster than all Picards, Mann, Ishikawa, Noor, SP, S, Picard-S, Garodia, K and K^*. It must be noted that it is also addressed by the AM^* iterative method, the effects of stability and data dependency on contraction mapping. In addition, the AM^* iterative method can be used to resolve differential equations with a time-delayed argument.