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Öğe A Robust Quintic Hermite Collocation Method for One-Dimensional Heat Conduction Equation(2024) Yagmurlu, Nuri Murat; Kutluay, Selçuk; Karakaş, Ali SercanIn this work, a new robust numerical solution scheme constructed on Quintic Hermite Collocation Method (QHCM) utilizing the traditional Crank-Nicolson type approximation technique is developed for solving 1D heat conduction equation with certain initial and boundary conditions which is mostly handled as a prototype equation to support the reliability of many proposed new numerical methods. All temporal and spatial quantities in the equation are fully discretized using a usual Crank-Nicolson type finite difference approximation and a QHCM, respectively. In obtaining the present scheme, all the roots of the fourth degree Legendre and Chebyshev polynomials shifted to the unit interval are used as suitable inner collocation points. The obtained results from the developed scheme are found to be good enough and better than those from other schemes encountered in the literature. The scheme is also shown to be unconditionally stable by Fourier stability test.Öğe A robust septic hermite collocation technique for dirichlet boundary condition Heat conduction equation(Sciendo, 2025) Kutluay, Selçuk; Yaǧmurlu, Nuri Murat; Karakaş, Ali SercanIn the current manuscript, approximate solution for 1D heat conduction equation will be sought with the Septic Hermite Collocation Method (SHCM). To achieve this goal, by means of the roots of both shifted Chebyschev and Legendre polynomials used at the inner collocation points, the pseudo code of the method is found out and applied using Matlab which is one of the widely utilized symbolic programming platforms. The unconditional stability of the scheme is shown by the traditional von-Neumann stability technique. To illustrate the accuracy and effectiveness of this newly current numerical scheme, a comparison among analytical and the computed numerical results is presented in tabular forms. It has been illustrated that the scheme is a both accurate and effective one and at the same time can be used in a successful way for finding out numerical solutions of several nonlinear problems as well as linear ones. © 2025 Selçuk Kutluay et al., published by Sciendo.Öğe Predictor - corrector yöntemi ve yakınsaklık analizi(İnönü Üniversitesi, 1987) Kutluay, Selçuk[Abtsract Not Available]
