arXiv subjects

Mehmet Giyas Sakar

Publications and source records attributed to Mehmet Giyas Sakar.

3 recordsLinked to original sources

arXiv2020

A new reproducing kernel approach for nonlinear fractional three-point boundary value problems

In this article, a new reproducing kernel approach is developed for obtaining numerical solution of nonlinear three-point boundary value problems with fractional order. This approach is based on reproducing kernel which is constructed by shifted Legendre polynomials. In considered problem, fractional derivatives with respect to $α$ and $β$ are defined in Caputo sense. This method has been applied to some examples which have exact solutions. In order to shows the robustness of the proposed method, some numerical results are given in tabulated forms.

math.NA↗

arXiv2018

Numerical solution of fractional Bratu type equations with Legendre reproducing kernel method

In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert space theory with shifted Legendre polynomials. Construction and convergence of iterative process are shown by orthogonal projection operator. Numerical results show that our method is effective and convenient for fractional Bratu type problem.

math.NA↗

arXiv2018

Numerical solution of time-fractional Burgers equation in reproducing kernel space

In this paper, we present an iterative reproducing kernel method for numerical solution of one dimensional fractional Burgers equation with variable coefficient. Convergence analysis is constructed theoretically. Numerical experiments show that approximate solution uniformly converges to exact solution. The results demonstrate that the given method very efficient and convenient for fractional Burgers equation.

math.NA↗