New Higher Order Multistep Methods for Solving Scalar Equations

We introduce and analyze two new multistep iterative methods with convergence order four and five based on modified homotopy perturbation methods, using the system of coupled equations involving an auxiliary function. We also present the convergence analysis and various numerical examples to demonstrate the validity and efficiency of our methods. These methods are a good addition and also a generalization of the existing methods for solving nonlinear equations.