The Solution of Initial-value Wave-like Models via Perturbation Iteration Transform Method

This work is based on the application of the new Perturbation Iteration Transform Method (PITM), which is a combined form of the Perturbation Iteration Algorithm (PIA) and the Laplace Transform (LT) method on some wave-like models with constant and variable coefficients. The method provides the solution in closed form, is efficient and it involves less computational work

ON APPROXIMATE AND CLOSED-FORM SOLUTION METHOD FOR INITIAL-VALUE WAVE-LIKE MODELS

This work presents a proposed Modified Differential Transform Method (MDTM) for obtaining both closed-form and approximate solutions of initial-value wave-like models with variable, and constant coefficients. Our results when compared with the exact solutions of the associated solved problems, show that the method is simple, effective and reliable. The results are very much in line with their exact forms. The method involves less computational work without neglecting accuracy. We recommend this simple proposed technique for solving both linear and nonlinear partial differential equations (PDEs) in other aspects of pure and applied sciences

Perturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model Equations

In this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead- Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree with those obtained via other semi-analytical methods viz: New Iterative Method and Adomian Decomposition Method. This present method proves to be very efficient and reliable. Mathematica 10 is used for all the computations in this stud