Abstract
In this article, we apply a generalized Vieta-Fibonacci (GVF) quasilinearization method to explore the numerical solution of third-order singular and nonlinear boundary value problems. Firstly, we use the quasilinearization technique to convert the governing nonlinear boundary value problem into a class of linearized equations. Then we build a collocation technique based on GVF functions to solve the resultant sequence of linearized equations. Convergence result of the method is established with respect to L 2 norm. Four test problems are considered to illustrate the applicability, efficiency and robustness of the proposed algorithm and to validate the theoretical estimate as well by comparing it with previous work.
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