In this work, a numerical technique for solving general nonlinear ordinary differential equations (ODEs) with variable coefficients and given conditions is introduced. The collocation method is used with rational Chebyshev (RC) functions as a matrix discretization to treat the nonlinear ODEs. Rational Chebyshev collocation (RCC) method is used to transform the problem to a system of nonlinear algebraic equations. The discussion of the order of convergence for RC functions is introduced. The proposed base is specified by its ability to deal with boundary conditions with independent variable that may tend to infinity with easy manner without divergence. The technique is tested and verified by two examples, then applied to four real life and applications models. Also, the comparison of our results with other methods is introduced to study the applicability and accuracy.

在这项工作中，介绍了一种求解具有可变系数和给定条件的一般非线性常微分方程 (ODE) 的数值技术。搭配方法与有理 Chebyshev (RC) 函数一起用作矩阵离散化来处理非线性 ODE。有理切比雪夫搭配 (RCC) 方法用于将问题转换为非线性代数方程组。介绍了 RC 函数收敛顺序的讨论。建议的基数由其处理具有自变量的边界条件的能力指定，该自变量可能以简单的方式趋于无穷大而不会发散。该技术通过两个例子进行测试和验证，然后应用于四个现实生活和应用模型。还，