Rational Chebyshev collocation method for solving nonlinear heat transfer equations

Abstract

In this paper, the classical collocation method has been revisited and modified by using the Chebyshev polynomials for solving nonlinear differential equations. Linear and nonlinear terms are converted to algebraical equations with the aid of the matrix relations. Resulting equations are solved to get unknown coefficients of rational Chebyshev polynomials. We apply the proposed technique for solving nonlinear heat transfer equations. Obtained results reveal that the rational Chebyshev collocation method can be safely applied to different types of nonlinear ordinary differential equations arising in science and engineering. © 2020 Elsevier Ltd