Abstract
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.
Highlights
1 Introduction As known, the nonlinear ordinary differential equations (ODEs) have an important role because of their applications in many fields of science and real life phenomena modeling for instance the logistic growth model in a population [1], the epidemic model [2], the kinetic model [3], the model of ozone decomposition [4], happiness dynamical models [5], the natural convection of Darcian fluid (NCDF) about a vertical full cone embedded in porous media (PM) with a prescribed wall temperature [6], and the Volterra population model [7]
Parand et al [27] and Ramadan et al [28] introduced rational Chebyshev (RC) functions for solving natural convection of Darcian fluid about a vertical full cone embedded in porous media with a prescribed wall temperature
The RC collocation method (RCC) as matrix discretization is introduced to obtain the solution of a general form of nonlinear ODEs defined on the semi-infinite domain
Summary
The nonlinear ordinary differential equations (ODEs) have an important role because of their applications in many fields of science and real life phenomena modeling for instance the logistic growth model in a population [1], the epidemic model [2], the kinetic model [3], the model of ozone decomposition [4], happiness dynamical models [5], the natural convection of Darcian fluid (NCDF) about a vertical full cone embedded in porous media (PM) with a prescribed wall temperature [6], and the Volterra population model [7]. The RC collocation method (RCC) as matrix discretization is introduced to obtain the solution of a general form of nonlinear ODEs defined on the semi-infinite domain. For more instances of the RC functions and their properties, we provide some suggested references for the reader [23, 30, 31]
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