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A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.doi:10.4236/jamp.2017.53053 fatcat:bb4bw7hj4jheles5laj32pzxdu