Abstract In this paper, we introduce two different methods based on Gegenbauer wavelet and Bernoulli wavelet for the solution of neutral delay differential equations. These methods convert linear and nonlinear neutral delay differential equations into system of linear and nonlinear algebraic equations, respectively. After solving these equations, we get the approximate solutions. Here, we have used the Gegenbauer wavelet (for different values of μ ) and Bernoulli wavelet and seen that both methods converge fast. We present six test problems consisting of five linear and one nonlinear, to illustrate the accuracy of present methods. Further, we compared our results with the results of existing methods present in the literature and seen that our methods gives more accurate results.

中文翻译：

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基于Gegenbauer和Bernoulli小波的求解中性延迟微分方程的搭配方法

摘要 本文介绍了两种不同的基于Gegenbauer 小波和Bernoulli 小波的求解中性延迟微分方程的方法。这些方法分别将线性和非线性中性延迟微分方程转化为线性和非线性代数方程组。求解这些方程后，我们得到近似解。在这里，我们使用了 Gegenbauer 小波（对于不同的 μ 值）和 Bernoulli 小波，并且看到两种方法收敛速度都很快。我们提出了六个测试问题，包括五个线性问题和一个非线性问题，以说明当前方法的准确性。此外，我们将我们的结果与文献中现有方法的结果进行了比较，发现我们的方法给出了更准确的结果。