Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations

• Main Authors: Mohamed A. Abd El Salam, Mohamed A. Ramadan, Mahmoud A. Nassar, Praveen Agarwal, Yu-Ming Chu
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Advances in Difference Equations
• Subjects: Nonlinear ordinary differential equations; Collocation method; Rational Chebyshev functions
• Online Access: https://doi.org/10.1186/s13662-021-03481-y

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.