arXiv subjects

Mohammad Reza Eslahchi

Publications and source records attributed to Mohammad Reza Eslahchi.

3 recordsLinked to original sources

arXiv2019

Müntz Pseudo Spectral Method: Theory and Numerical Experiments

This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-Müntz functions presented by the authors recently. These basis functions are, in fact, generalizations form of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.

math.NA↗

arXiv2019

Müntz Sturm-Liouville Problems: Theory and Numerical Experiments

This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on. With respect to these functions two new orthogonal projections and their error bounds are derived. Also, two new Müntz type quadrature rules are introduced. As two applications of these basis functions some fractional ordinary and partial differential equations are considered and numerical results are given.

math.NA↗

arXiv2019

Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery

The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolics, one elliptic and one ordinary differential equations that are coupled together and describe the growth of a plaque in the artery. We start our discussion by using the front fixing method to fix the free domain and simplify the model by changing the mix boundary condition to a Neumann one by applying suitable changes of variables. Then, after employing a nonclassical finite difference and the collocation method on this model, we prove the stability and convergence of methods. Finally, some numerical results are considered to show the efficiency of the method.

math.NA↗