Deniz Agirseven

An analytical study for Fisher type equations by using homotopy perturbation method

In this paper, homotopy perturbation method is applied to Fisher type equations. The solutions introduced in this study are in recursive sequence forms which can be used to obtain the closed form of the solutions if they are required. The method is tested on various examples which are revealing the effectiveness and the simplicity of the method.

Well-posedness of delay parabolic difference equations

The well-posedness of difference schemes of the initial value problem for delay differential equations with unbounded operators acting on delay terms in an arbitrary Banach space is studied. Theorems on the well-posedness of these difference schemes in fractional spaces are proved. In practice, the coercive stability estimates in Hölder norms for the solutions of difference schemes of the mixed problems for delay parabolic equations are obtained.

Finite Difference Method for Delay Parabolic Equations

A finite difference method for the approximate solution of the initial‐boundary value problem for the delay parabolic partial differential equation is considered. Stable difference schemes of first and second orders of accuracy for this problem are studied. The stability estimates for the solution of these difference schemes in Holder norms are obtained. The theoretical statements for the solution of these difference schemes are supported by numerical examples.

Well-posedness of delay parabolic equations with unbounded operators acting on delay terms

In the present paper, the well-posedness of the initial value problem for the delay differential equation dv(t)dt+Av(t)=B(t)v(t−ω)+f(t), t≥0; v(t)=g(t) (−ω≤t≤0) in an arbitrary Banach space E with the unbounded linear operators A and B(t) in E with dense domains D(A)⊆D(B(t)) is studied. Two main theorems on well-posedness of this problem in fractional spaces Eα are established. In practice, the coercive stability estimates in Hölder norms for the solutions of the mixed problems for delay parabolic equations are obtained.MSC:35G15.

Approximate solutions of delay parabolic equations with the Neumann condition

An approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation is considered. Stable difference schemes of first and second orders of accuracy for this problem are investigated. Convergence estimates for the solution of these difference schemes in Holder norms are established. Theoretical statements are supported by numerical examples.

He's homotopy perturbation method for fourth-order parabolic equations

In this paper, Hes homotopy perturbation method is applied to fourth-order parabolic partial differential equations with variable coefficients to obtain the analytic solution. The method is tested on six examples, which reveal its effectiveness and simplicity.

Bounded solutions of delay nonlinear evolutionary equations

We consider the initial value problem { d u d t + A u ( t ) = f ( u ( t ) , u ( t - w ) ) , t ź 0 , u ( t ) = ź ( t ) , - w ź t ź 0 in a Banach space E with the positive operator A . Theorem on the existence and uniqueness of a bounded solution of this problem is established for a nonlinear evolutionary equation with time delay. The application of the main theorem for four different nonlinear partial differential equations with time delay is shown. The first and second order of accuracy difference schemes for the solution of one dimensional nonlinear parabolic equation with time delay are presented. Numerical results are provided.

On the stability of the telegraph equation with time delay

In this study, the initial value problem for telegraph equations with delay in a Hilbert space is considered. Theorem on stability estimates for the solution of this problem is established. As a test problem, one-dimensional delay telegraph equation with Dirichlet boundary conditions is considered. Numerical solutions of this problem are obtained by first and second order of accuracy difference schemes.

Difference Schemes for Delay Parabolic Equations with Periodic Boundary Conditions

The initial-boundary value problem for the delay parabolic partial differential equation with nonlocal conditions is studied. The convergence estimates for solutions of first and second order of accuracy difference schemes in Holder norms are obtained. The theoretical statements are supported by a numerical example.