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A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments
(Hindawi Ltd, 2014) Koc, Ayse Betul; Cakmak, Musa; Kurnaz, Aydin
A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
A new Fibonacci type collocation procedure for boundary value problems
(Springeropen, 2013) Koc, Ayse Betul; Cakmak, Musa; Kurnaz, Aydin; Uslu, Kemal
In this study, we present a new procedure for the numerical solution of boundary value problems. This approach is mainly founded on the Fibonacci polynomial expansions, the so-called pseudospectral methods with the collocation method. The applicability and effectiveness of our proposed approach is shown by some illustrative examples. Then, the results indicate that this method is very effective and highly promising for linear differential equations defined on any subinterval of the real domain. MSC: 35A25.