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Öğe First boundary value problem for cordes-type semilinear parabolic equation with discontinuous coefficients(Hindawi, 2020-06-19) Harman, Aziz; Harman, EzgiFor a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj-ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n-1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n-1,n≥2.Öğe Comparing numerical methods for solving time-fractional reaction-diffusion equations(Hindawi, 2012-08-29) Turut, Veyis; Güzel, NuranMultivariate Pade approximation ´ MPA is applied to numerically approximate the solutions of time-fractional reaction-diffusion equations, and the numerical results are compared with solutions obtained by the generalized differential transform method GDTM. The fractional derivatives are described in the Caputo sense. Two illustrative examples are given to demonstrate the effectiveness of the multivariate Pade approximation ´ MPA. The results reveal that the multivariate Pade approximation ´ MPA is very effective and convenient for solving timefractional reaction-diffusion equationsÖğe On solving partial differential eqauations of fractional order by using the variational iteration method and multivariate padé approximation(European Journal of Pure and Applied Mathematics, 2013-04) Turut, Veyis; Güzel, NuranIn this article, multivariate Padé approximation and variational iteration method proposed by He is adopted for solving linear and nonlinear fractional partial differential equations. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include nonlinear timefractional hyperbolic equation and linear fractional Klein-Gordon equation are investigated to show efficiency of multivariate Padé approximation. Comparison of the results obtained by the variational iteration method with those obtained by multivariate Padé approximation reveals that the present methods are very effective and convenient.Öğe Multivariate pade approximations for solving nonlinear diffusion equations(Walter de Gruyter, 2015-11-24) Turut, VeyisIn this paper, multivariate Pade approximation is applied to power series solutions of nonlinear diffusion equations. As it is seen from tables, multivariate Pade approximation (MPA) gives reliable solutions and numerical results.Öğe Rational approximatons for solving cauchy problems(2016-08-16) Turut, Veyis; Bayram, MustafaIn this letter, numerical solutions of Cauchy problems are considered by multivariate Pad´e approximations (MPA). Multivariate Pad´e approximations (MPA) were applied to power series solutions of Cauchy problems that solved by using He’s variational iteration method (VIM). Then, numerical results obtained by using multivariate Pad´e approximations were compared with the exact solutions of Cauchy problems.Öğe Some new theorems in hilbert quasilinear spaces(Van Yüzüncü Yıl Üniversitesi, 2015) Bozkurt, Hacer; Yılmaz, YılmazThis study is concerned with the some new theorems and deÖnitions in Hilbert quasilinear spaces. First, we introduce minimizing vector theorem and some results in Hilbert quasilinear spaces. Next, we provide two main examples: First example is a Hilbert quasilinear space, that does not satisfy the orthogonal decomposition and second example is subset of a Hilbert quasilinear space with the orthogonal decomposition properties. Then, we have from Örst example that any Hilbert quasilinear space may not satisfy the orthogonal decomposition theorem of Hilbert spaces. Finally, we give some results related to above theorems provide an important contributions to the improvement of the quasilinear functional analysis.Öğe Multivariate padé approximation for solving nonlinear partial differential equations of fractional order(Hindawi, 2013-03-16) Turut, Veyis; Güzel, NuranTwo tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Pade approximation (MPA), for ´ solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM), then power series solution of fractional differential equation was put into multivariate Pade series. Finally, numerical results were ´ compared and presented in tables and figuresÖğe Numerical approximatons for solving partial differentıal equations with variable coefficients(Science Publishing Group, 2013-02-20) Turut, VeyisIn this paper, variational iteration method (VIM) and multivariate padé approximaton (MPA) were compared. First, partial differential eqaution has been solved and converted to power series by variational iteration method (VIM), then the numerical solution of partial differential eqauation was put into multivariate padé series. Thus the numerical solutions of the partial differential eqautions were obtained. Numerical solutions of two examples were calculated and results were presented in tables and figures.
