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A Taylor Series Based Method for Solving Nonlinear Sine -Gordon and Klein-Gordon Equations

3 Abstract: In this paper, Taylor series based on which is the differential transform method (DTM) is applied to solve various forms of nonlinear Klein-Gordon type equations. The application of differential transform method is extended to derive approximate analytical solutions of nonlinear Klein-Gordon type equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The results show that the approach is easy to implement and accurate when applied to these type equations. The method introduces a promising tool for solving many linear and nonlinear differential equations.