Fibonacci collocation method for solving a class of nonlinear differential equations

Abstract

In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.