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Öğe The Analytical and a Higher-Accuracy Numerical Solution of a Free Boundary Problem in a Class of Discontinuous Functions(Hindawi Ltd, 2012) Sinsoysal, BahaddinA new method is suggested for obtaining the exact and numerical solutions of the initial-boundary value problem for a nonlinear parabolic type equation in the domain with the free boundary. With this aim, a special auxiliary problem having some advantages over the main problem and being equivalent to the main problem in a definite sense is introduced. The auxiliary problem allows us to obtain the weak solution in a class of discontinuous functions. Moreover, on the basis of the auxiliary problem a higher-resolution numerical method is developed so that the solution accurately describes all physical properties of the problem. In order to extract the significance of the numerical solutions obtained by using the suggested auxiliary problem, some computer experiments are carried out.Öğe The D'Alembert Type Solution of the Cauchy Problem for the Homogeneous with Respect to Fourth Order Derivatives for Hyperbolic Equation(Springer International Publishing Ag, 2017) Rasulov, Mahir; Aslan, Zafer; Sinsoysal, Bahaddin; Bal, HakanIn this paper the D'Alembert type solution for the following Sigma(i=0) a(i) partial derivative(4)u (x, t)/partial derivative t(4)-(i)partial derivative x(i) = 0, partial derivative(k) u(x, t)/partial derivative t(k) |(t=0) = phi(k) (x), (k = 0, 1, 2, 3) Cauchy problem is constructed. Here, a(i), (i = 1, 2, 3, 4) and fk (x), (k = 1, 2, 3, 4) are given constants and functions, respectively. The cases where the roots of the characteristic equation are folded are examined and compact expressions for the solutions are obtained. The obtained solutions allow proving the uniqueness and existence of the solutions of the considered problem.Öğe Diferansiyel Denklemler Sisteminin Rezidü Çözümü ve Sabit Gerilim Kaynaklı RC Devresi Problemine Uygulanması(Beykent Üniversitesi, 2013) Sinsoysal, Bahaddin; Rasulov, MahirMakalede sabit katsayılı adi diferansiyel denklemler sistemi için yazılmış Cauchy probleminin rezidü metodu ile gerçek çözümü elde edilmiş ve söz konusu metot uygulanarak sabit gerilimli bir RC devre probleminin çözümünün bulunması için uygulanmıştır.Öğe D’alembert’s Solution Of The Initial Value Problem For The Third-Order Linear Hyperbolic Equation(Beykent Üniversitesi, 2019) Günerhan, Duygu; Sinsoysal, BahaddinIt is well known that the famous D’Alembert formula for solving the wave equation of secondorder is a very important instrument in the study of the dynamics of waves. It is also obvious that D’Alembert’s solutions for higher-order partial differential equations are of great importance. In this paper, the D’Alembert solutions of the Cauchy problem for linear partial differential equations with homogeneous constant coefficients of the third-order are obtained. Finally, using the obtained solutions, some computer tests on three distinct roots have been carried out. The results clearly indicate the dispersion dynamics of waves with some initial profile.Öğe Efficient Numerical Method of the 1D Motion of Two-Phase Fluid through Porous Medium in a Class of Discontinuous Functions(Springer-Verlag Berlin, 2009) Sinsoysal, Bahaddin; Rasulov, MahirIn this paper a new numerical method for nonlinear system of partial differential equations which describes motion of a two-phase compressible fluid in microscopic porous medium in a class of discontinuous functions is suggested. For this aim, at first, the system of equations is split in two equations according to physical parameters. First one with respect to water saturation, and the other one with respect to pressure. Then, the special auxiliary problem having some advantages over the main problem is introduced. This auxiliary problem permits to develop the efficient numerical algorithm for obtaining the solution. Using the solution of the auxiliary problem, the solution of the main problem, which expresses all the physical properties is found.Öğe Finite Differences Method for One Dimensional Nonlinear Parabolic Equation with Double Nonlinearity(Springer-Verlag Berlin, 2013) Sinsoysal, Bahaddin; Coruhlu, TurgayThe finite differences scheme for finding a numerical solution of the parabolic equation with double nonlinearity is suggested. For this purpose a special auxiliary problem having some advantages over the main problem is introduced. Some properties of the numerical solution are studied and using the advantages of the proposed auxiliary problem, the convergence of the numerical solution to the exact solution in the sense of mean is proven.Öğe The Finite Differences Schemes For First Order Nonlinear System Equations In A Class Of Discontinuous Functions(Beykent Üniversitesi, 2007) Rasulov, Mahir; Sinsoysal, BahaddinIn this paper a new finite differences schemes of the Cauchy and initialboundary value problem, for the first order system differential equations which describe some conservation laws is suggested. At first an auxiliary problem which is equivalent to the main problem in certain sense is introduced. On the basis of the auxiliary problem the simple and economical algorithms from computational point of view are proposed.Öğe A Higher-Order Sensitive Finite Differences Scheme Of The Cauchy Problem For 2D Linear Hyperbolic Equations With Constant Coefficients In A Class Of Discontinuous Functions(Beykent Üniversitesi, 2020) Yener, Öykü; Sinsoysal, Bahaddin; Mahir, RasulovIn this study we develop a finite difference scheme for practical calculation of the Cauchy problem for the 2D scalar advection equation with a higher accuracy order constant coefficient, encountered in different fields of hydrodynamics. For this aim, to develop an auxiliary problem having some advantages over the main problem is introduced. The proposed auxiliary problem permits us to construct a higher-order sensitive finite differences scheme.Öğe Investigating the Dynamics of Traffic Flow on a Highway in a Class of Discontinuous Functions(Springer-Verlag Berlin, 2015) Sinsoysal, Bahaddin; Bal, Hakan; Sahin, E. IlhanThis work is devoted to finding a solution of Riemann problem for the first order nonlinear partial equation which describes the traffic flow on highway. When rho(l) > rho(r), the solution is presented as a piecewise continuous function, where rho(l) and rho(r) are the densities of cars on the left and right side of the intersection respectively. On the contrary case, a shock of which the location is unknown beforehand arises in the solution. In this case, a special auxiliary problem is introduced, the solution of which makes it possible to write the exact solution showing the locations of shock. For the realization of the proposed method, the parameters of the flow are also found.Öğe Numerical Solution of Nonlinear Parabolic Type Equation in the Class of Generalized Functions with Degeneration(Amer Inst Physics, 2018) Sinsoysal, Bahaddin; Bal, Hakan; Yilmaz, KubraIn this paper, a method for obtaining the numerical solution of the first type initial boundary value problem for a second order degenerate parabolic equation is suggested. To this end, in accordance with the smoothness of the solution of the investigated problem, we introduce an auxiliary problem, as it has some advantages over the main problem, and is equivalent to the main problem in a definite sense. Using the introduced auxiliary problem, we write a more sensitive numerical scheme whose solution expresses all of the physical properties of the problem accurately. Moreover, using the auxiliary problem, we can write the higher order numerical schemes with respect to the time variable.Öğe Örgüt Kültürü İle Örgütsel Yenilikçilik Arasındaki İlişkide Örgütsel Öğrenmenin Aracı Rolü(Kafkas Üniversitesi, İktisadi ve İdari Bilimler Fakültesi, 2019) Kendir, Vasfi; Sinsoysal, Bahaddin; Orçanlı, Kenan; Boztoprak, HasanYapılan çalışmanın amacı, örgüt kültürü (ÖK) ile örgütsel yenilikçilik (ÖY) değişkenleri arasındaki ilişkide örgütsel öğrenme (ÖÖ) değişkeninin aracılık rolünün olup olmadığını belirlemektir. Söz konusu çalışmada kullanılan veriler, bir ünivesite hastanesinde 600 personeline uygulanan üç adet ölçek ile toplanmış ve kurulan modelin analizi hiyerarşik regresyon modeli ile test edilmiştir. Yapılan çalışma sonucu, ÖÖ'nin; ÖK ile ÖY değişkenleri arasında kısmi aracılık rolüne sahip olduğu sonucuna ulaşılmıştır. Kısmi aracılık etkisi olan değişkenlerin arasındaki ilişkiler ile ilgili olarak yapılan Sobel testi sonucunda; ÖK ile ÖY değişkenleri arasında ilişkinin anlamlı bir ilişki ve bu değişkenler arasında da ÖÖ değişkeninin kısmi aracılık etkisinin olduğu teyit edilmiştir.Öğe Otobanlarda Trafik Akış Dinamiğinin İncelenmesi(Beykent Üniversitesi, 2014) Carfi, Hasan; Sinsoysal, BahaddinMakalede otobanlardaki trafik akışının dinamiğini düzgün aksettiren matematiksel bir model oluşturulmuştur. p? ve pr sırasıyla arakesitin sağ ve sol tarafındaki araç yoğunluğunu göstermek üzere, p? > pr durumunda çözümün parçalı sürekli bir fonksiyon olduğu gözlenmiştir. Aksi halde, çözümde yeri önceden bilinmeyen bir şokun meydana geldiği ispatlanmış ve sıçrayışın yerinin bulunması için bir metot önerilmiştir. İlaveten önerilen metodun gerçekleştirilmesi için akış parametreleri de bulunmuşturÖğe Residue Method for The Solution of Heat Equation with Nonlocal Boundary Condition(Beykent Üniversitesi, 2008) Rasulov, Mahir; Sinsoysal, BahaddinIn this paper by using the residue method, the exact solution of mixed problem for linear heat equation with nonlocal boundary conditions is obtained. For this aim, at first, the formula for expansion of an arbitrary function in a series of residues of the solution of the corresponding spectral problem is proved. Further, this formula is used to show that if the mixed boundary-value problem in question has a sufficiently smooth solution, this solution can be represented by the given residue formula.Öğe Solutions of a 1-D Conservation Laws without Convexity(Beykent Üniversitesi, 2012) Resulov, Mahir; Sinsoysal, BahaddinIn this paper the exact solution for Cauchy problem of first order nonlinear partial equation with piece-wise initial condition described scalar conservation laws without convexity of the state function. In particular, the state functions having four and one point of inflection are considered. The structure of solutions is investigated.
