Interest in the construction of efficient methods for solving initial value\nproblems that have some peculiar properties with it or its solution is recently\ngaining wide popularity. Based on the assumption that the solution is representable\nby nonlinear trigonometric expressions, this work presents an explicit\nsingle-step nonlinear method for solving first order initial value problems\nwhose solution possesses singularity. The stability and convergence properties\nof the constructed scheme are also presented. Implementation of the new\nmethod on some standard test problems compared with those discussed in\nthe literature proved its accuracy and efficiency.
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