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Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

机译:生理学中非线性奇异边值问题的近似级数解

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摘要

We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.
机译:我们介绍了一种基于Adomian分解方法(ADM)的有效递归方案,用于解决非线性奇异边值问题。此方法基于对ADM的修改;在这里,在建立求解分量的递归方案之前,我们使用所有边界条件来导出积分方程。实际上,我们在计算解决方案组成部分时开发了没有任何不确定系数的递归方案。与经典ADM不同,该方法避免了求解不确定系数的非线性代数或先验方程序列。近似解以具有易于计算的组件的级联形式获得。讨论了解决方案的唯一性。建立了该方法的收敛性和误差分析。通过四个数值例子验证了该方法的准确性和可靠性。

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