Orthogonal polynomials

Orthogonal collocation

Physics

Chebyshev polynomials

Mathematical analysis

Chebyshev equation

Nonlinear system

Chebyshev iteration

Collocation method

Chebyshev filter

Classical orthogonal polynomials

Applied mathematics

Mathematics

Ordinary differential equation

Quantum mechanics

Differential equation

Advances in Difference Equations

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.

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