Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar
A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar
Turkish Journal of Mathematics
This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating $y^{\prime}(u)$ using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to …
Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim
Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim
Turkish Journal of Mathematics
In this study, the approximate solution of the nonlinear differential equation with variable delays is investigated by means of a collocation method based on the truncated Pell-Lucas series. In the first stage of the method, the assumed solution form (the truncated Pell-Lucas polynomial solution) is expressed in the matrix form of the standard bases. Next, the matrix forms of the necessary derivatives, the nonlinear terms, and the initial conditions are written. Then, with the help of the equally spaced collocation points and these matrix relations, the problem is reduced to a system of nonlinear algebraic equations. Finally, the obtained system …
Numerical Solution For Benjamin-Bona-Mahony-Burgers Equation With Strang Time-Splitting Technique, Meli̇ke Karta
Numerical Solution For Benjamin-Bona-Mahony-Burgers Equation With Strang Time-Splitting Technique, Meli̇ke Karta
Turkish Journal of Mathematics
In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the …