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In this work, an efficient approximation scheme has been proposed for gettingaccurate approximate solution of nonlinear partial differential equations withconstant or variable coefficients satisfying initial conditions in a series ofexponential instead of an algebraic function of independent variables. As aconsequence: i) the convergence of the series found to be faster than the sameobtained by few other methods and ii) the exact analytic solution can beobtained from the first few terms of the series of the approximate solution, incases the equation is integrable. The convergence of the sum of the successivecorrection terms has been established and an estimate of the error in theapproximation has also been presented. The efficiency of the present method hasbeen illustrated through some examples with a variety of nonlinear termspresent in the equation.

A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations