In this work, we propose a numerical framework for solving a class of Lienard’s equation. This equation arises in the development of radio and vacuum tube technology. The spatial approximation is based on the Bernoulli collocation method in which the shifted Chebyshev collocation points are used as collocation nodes. The operational matrix of derivatives of Bernoulli is introduced. The matrix together with the collocation method is then utilized to reduce the problem into a system of nonlinear algebraic equations. Also, a reliable and fast approach for solving this nonlinear system is discussed. The error function is presented to assure the accuracy of the solution. Numerical results and comparisons with other existing methods provided in the literature are made proving the ability of the proposed scheme of providing excellent results.

中文翻译：

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一种快速有效的求解一类非线性Lienard方程的方案

在这项工作中，我们提出了一个求解一类Lienard方程的数值框架。这个方程式出现在无线电和真空管技术的发展中。空间近似基于伯努利搭配方法，其中将偏移的切比雪夫搭配点用作搭配节点。介绍了伯努利衍生物的运算矩阵。然后将矩阵与搭配方法一起用于将问题简化为非线性代数方程组。此外，讨论了一种可靠且快速的方法来解决该非线性系统。提供误差函数以确保解决方案的准确性。数值结果和与文献中提供的其他现有方法的比较证明了所提方案提供出色结果的能力。