A New Strategy for the Approximate Solution of Hyperbolic Telegraph Equations in Nonlinear Vibration System

Abstract

This study examines a new approach for the approximate solution of hyperbolic telegraph equations emerging in magnetic fields and electrical impulse transmissions. We introduce a Laplace-Carson transform coupled with the homotopy perturbation method which is called the Laplace-Carson homotopy perturbation method ( ${\mathcal{L}}_c$ -HPM). The most significant feature of this approach is that we do not require any restriction of variables and hypotheses to find the results of nonlinear problems. Further, HPM using He’s is applied to reduce the number of computations in nonlinear terms. We demonstrate some graphical results to show that ${\mathcal{L}}_c$ -HPM is a simple and suitable approach for linear and nonlinear problems.