TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/4
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Article The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics(2019-03-31) Kürkçü, Ömür Kıvanç; Dönmez Demir, Duygu; Sezer, Mehmet; Çınardalı, Tuğçe; Demir, Duygu DönmezIn this study, the Legendre operational matrix method based on collocation points is introduced to solve high order ordinary differentialequations with some nonlinear terms arising in physics and mechanics. This technique transforms the nonlinear differential equationinto a matrix equation with unknown Legendre coefficients via mixed conditions. This solution of this matrix equation yields theLegendre coefficients of the solution function. Thus, the approximate solution is obtained in terms of Legendre polynomials. Some testproblems together with residual error estimation are given to show the usefulness and applicability of the method and the numericalresults are compared.Article A NEW NUMERICAL METHOD FOR SOLVING DELAY INTEGRAL EQUATIONS WITH VARIABLE BOUNDS BY USING GENERALIZED MOTT POLYNOMIALS(2018-10-31) Kürkçü, Ömür KıvançIn this study, the delay integral equations with variable bounds are considered and their approximate solutions are obtained byusing a new numerical method based on matrices, collocation points and the generalized Mott polynomials including aparameter- ? . An error analysis technique consisting of the residual function is performed. The numerical examples are appliedto illustrate the practicability and usability of the method. The behavior of the solutions is monitored in terms of the parameter-? . The accuracy of the method is scrutinized for different values of N and also the numerical results are discussed in figuresand tables.