Our aim in this paper is to propose an SOR-like new iterative method by introducing a relaxation parameter to improve the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [J. Math. Anal. Appl. 316 (2006) 753–763] in order to solve two problems. The first one is the problem of the spread of a nonfatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of prey and predator. The proposed method is not limited to these two problems but can be applicable to a wide range of systems of nonlinear functional problem. The results, for different values of , show that we found some known methods and our method compared to methods using the calculation of special polynomials and derivatives like the Adomian decomposition method (ADM), the calculation of the Lagrange multiplier as in the variational iterative method (VIM), or the construction of a homotopy as in the homotopy perturbation method (HPM) has several advantages, such as very effective and very simple to implement. Unfortunately, these methods do not guarantee a valid approximation in large time interval. To overcome this, we applied our method for approximating the solution of the problems in a sequence of time intervals as a multistage approach. Some numerical results are presented with plots according to the parameter .

中文翻译：

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类似于SOR的新的求解流行模型和食饵与捕食者问题的迭代方法

我们的目标是通过引入松弛参数来提出一种类似于SOR的新迭代方法，以改进Daftardar-Gejji和Jafari（NIM）提出的新迭代方法。数学。肛门 应用 316（2006）753–763]以解决两个问题。第一个问题是非致命疾病在人口中的传播问题，假定该人群在流行期间具有恒定的规模，第二个问题是猎物和捕食者的问题。所提出的方法不限于这两个问题，而是可以适用于广泛的非线性功能问题的系统。结果，对于的不同值，表明我们发现了一些已知方法，并且与使用特殊多项式和导数的方法相比，例如Adomian分解方法（ADM），拉格朗日乘数的计算（如变分迭代法（VIM）或构造同态摄动法（HPM）中的同态具有多个优点，例如非常有效且易于实现。不幸的是，这些方法不能保证大时间间隔内的有效逼近。为了克服这个问题，我们采用了一种方法，以一种多阶段的方法来对一系列时间间隔中的问题进行近似求解。根据参数给出了一些数值结果。