arXiv subjects

Raziyeh Dehbozorgi

Publications and source records attributed to Raziyeh Dehbozorgi.

3 recordsLinked to original sources

arXiv2020

Galerkin Finite Element Method for Nonlinear Fractional Differential Equations

In this paper, we study the existence, regularity, and approximation of the solution for a class of nonlinear fractional differential equations. {In order to do this}, suitable variational formulations are defined for a nonlinear boundary value problems with Riemann-Liouville and Caputo fractional derivatives together with the homogeneous Dirichlet condition. We {investigate} the well-posedness and also the regularity of the corresponding weak solutions. Then, we develop a Galerkin finite element approach {\color{blue}for} the numerical approximation of the weak formulations and {drive a priori error estimates and prove the stability of the schemes}. Finally, some numerical experiments are provided to {demonstrate} the accuracy of the proposed method.

math.NA↗

arXiv2020

Numerical Solution of Nonlinear Abel Integral Equations: An $ hp $-Version Collocation Approach

This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of the nonlinear Abel integral equations is studied completely. An $hp$-version collocation method in conjunction with Jacobi polynomials is introduced so as an appropriate numerical solution to be found. We analyze it properly and find an error estimation in $L^2$-norm. The efficiency of the method is illustrated by some numerical experiments.

math.NA↗

arXiv2019

$ hp $-version collocation method for a class of nonlinear Volterra integral equations of the first kind

In this paper, we present a collocation method for nonlinear Volterra integral equation of the first kind. This method benefits from the idea of $hp$-version projection methods. We provide an approximation based on the Legendre polynomial interpolation. The convergence of the proposed method is completely studied and an error estimate under the $L^2$-norm is provided. Finally, several numerical experiments are presented in order to verify the obtained theoretical results.

math.NA↗