Abstract In this paper, a nonstandard finite difference scheme is employed to approximate the solution of a nonlinear second order differential equation obtained from the model of heat transfer in extended surfaces. The proposed method for the system enjoys the nonlocal approximation of nonlinear terms and requires neither any iterative procedure nor the computation of Jacobian unlike the standard finite difference method. Accuracy of the method and conditions for generating expected positive solution are also discussed in detail.

中文翻译：

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广义 Fins 问题的非标准有限差分近似

摘要 本文采用非标准有限差分格式来逼近由扩展表面传热模型获得的非线性二阶微分方程的解。该系统所提出的方法享有非线性项的非局部逼近，并且不需要任何迭代过程，也不需要与标准有限差分方法不同的雅可比矩阵计算。还详细讨论了生成预期正解的方法和条件的准确性。