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The Klein-Gordon equation is used to model many nonlinear phenomena. In this paper, an analytic solution of the Klein-Gordon equation is obtained by using a new modification of the homotopy perturbation method (NHPM). Theoretical considerations are discussed. The results reveal that the method is explicit, effective, and easy to use. [ABSTRACT FROM AUTHOR]

In this work, a new modified homotopy perturbation (NHPM) is applied to solve a special kind of nonlinear Volterra integral equations in two-dimensional space. The two most important steps in the application of the new Homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. In the present paper, convergence of the new approach is proved. Comparison of our solution with the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) shows that the NHPM is effective and accurate in solving these kind of problems. [ABSTRACT FROM AUTHOR]

In this paper, a new form of homotopy perturbation method (NHPM) has been adopted for solving second- rder linear hyperbolic telegraph equation. This new approach leads to the exact solution of one- or two-dimensional second-order hyperbolic equation. Computations of the examples reveal the simplicity and fewer manipulations in comparison with the usual method. [ABSTRACT FROM AUTHOR]