Elyas Shivanian - Academia.edu (original) (raw)

Uploads

Papers by Elyas Shivanian

Research paper thumbnail of On The Existence of Multiple Solutions of a Class of Third-Order Nonlinear Two-Point Boundary Value Problems

Mediterranean Journal of Mathematics, 2015

Research paper thumbnail of A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs

Zeitschrift für Naturforschung A, 2015

This paper presents a meshless method which, at the first step, utilises the radial basis functio... more This paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.

Research paper thumbnail of Application of the Variational Iteration Method to Nonlinear Volterra’s Integro-Differential Equations

Zeitschrift für Naturforschung A, 2008

Research paper thumbnail of Chapter 2: Predictor Homotopy Analysis Method (PHAM)

Advances in the Homotopy Analysis Method, 2013

Research paper thumbnail of Bio-inspired computing platform for reliable solution of Bratu-type equations arising in the modeling of electrically conducting solids

Applied Mathematical Modelling, 2016

Research paper thumbnail of Reliable numerical treatment of nonlinear singular Flierl–Petviashivili equations for unbounded domain using ANN, GAs, and SQP

Applied Soft Computing, 2015

Research paper thumbnail of Accepted Manuscript Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping

Please cite this article in press as: V.R. Hosseini et al., Local radial point interpolation (MLR... more Please cite this article in press as: V.R. Hosseini et al., Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping, J. Comput. Phys. (2016), http://dx. Abstract The purpose of the current investigation is to determine numerical solution of time-fractional diffusion-wave equation with damping for Caputo's fractional derivative of order α(1 < α ≤ 2). A meshless local radial point interpolation (MLRPI) scheme based on Galerkin weak form is analyzed. The reason of choosing MLRPI approach is that it dose not require any background integrations cells, instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape. The unconditional stability and convergence with order O(τ 6−2α) are proved, where τ is time stepping. Also, Several numerical experiments are illustrated to verify theoretical analysis.

Research paper thumbnail of Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping

Journal of Computational Physics, 2016

Research paper thumbnail of Monomial geometric programming with fuzzy relation inequality constraints with max-product composition

Computers and Industrial Engineering, May 1, 2009

Research paper thumbnail of Optimization of Linear Objective Function Subject to Fuzzy Relation Inequalities Constraints with Max-Average Composition

Iranian Journal of Fuzzy Systems, 2007

ABSTRACT In this paper, the finitely many constraints of a fuzzy relation inequalities problem ar... more ABSTRACT In this paper, the finitely many constraints of a fuzzy relation inequalities problem are studied and the linear objective function on the region defined by a fuzzy max-average operator is optimized. A new simplification technique which accelerates the resolution of the problem by removing the components having no effect on the solution process is given together with an algorithm and a numerical example to illustrate the steps of the problem resolution process.

Research paper thumbnail of Solution of singular linear vibrational BVPs by the homotopy analysis method

ABSTRACT In this paper, the homotopy analysis method (HAM) which is a powerful technique of nonli... more ABSTRACT In this paper, the homotopy analysis method (HAM) which is a powerful technique of nonlinear analysis, is examined in the solution of the linear vibration equation for very a large circular membrane. The method is shown to be able to handle a variety of pertaining singular boundary value problems (BVPs), to allow for graphical presentation of the results, and appears to be a viable alternative to applicable integral transform methods.

Research paper thumbnail of sdfadfA nonlinear partial integro-differential equation arising in population dynamic via radial basis functions and theta-method

Research paper thumbnail of A nonlinear partial integro-differential equation arising in population dynamic via radial basis functions and theta-method

ABSTRACT This paper proposes a numerical method to deal with the integro-differential reaction-di... more ABSTRACT This paper proposes a numerical method to deal with the integro-differential reaction-diffusion equation. In the proposed method, the time variable is eliminated by using finite difference theta− method to enjoy the stability condition. The method benefits from collocation radial basis function method, the generallized thin plate splines (GTPS) radial basis functions are used. Therefore, it does not require any struggle to determine shape parameter. The obtained results for some numerical examples reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.

Research paper thumbnail of Meshless local Petrov–Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation

Engineering Analysis with Boundary Elements, 2015

Research paper thumbnail of Multiplicity results and closed-form solution for catalytic reaction in a flat particle

Journal of the Taiwan Institute of Chemical Engineers, 2015

Research paper thumbnail of On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations

International Journal for Numerical Methods in Engineering, 2015

Research paper thumbnail of Analysis of meshless local and spectral meshless radial point interpolation (MLRPI and SMRPI) on 3-D nonlinear wave equations

Ocean Engineering, 2014

ABSTRACT In this paper, the meshless local radial point interpolation (MLRPI) method is applied t... more ABSTRACT In this paper, the meshless local radial point interpolation (MLRPI) method is applied to simulate three space dimensional nonlinear wave equation of the form utt+αut+βu=uxx+uyy+uzz+δg(u)ut+f(x,y,z,t)utt+αut+βu=uxx+uyy+uzz+δg(u)ut+f(x,y,z,t), 0&lt;x,y,z&lt;1,t&gt;0 subject to given appropriate initial and Dirichlet boundary conditions and then a new spectral meshless radial point interpolation (SMRPI) method is proposed to solve the mentioned problem. The main drawback of methods in fully 3-D problems is the large computational costs. In the MLRPI method, all integrations are carried out locally over small quadrature domains of regular shapes such as spheres or cubes. In innovative SMRPI method, it is not needed to any integration. The radial point interpolation method is proposed to construct shape functions for MLRPI and basis functions for SMRPI. A weak formulation with a Heaviside step function transforms the set of governing equations into local integral equations on local subdomains in MLRPI whereas the operational matrices converts easily the governing equations (even high order) into linear system of equations in SMRPI. A two-step time discretization method is employed to approximate the time derivatives. To treat the nonlinearity part, a kind of predictor–corrector scheme combined with one-step time discretization and Crank–Nicolson technique is adopted. A comparison study of the efficiency and accuracy of the MLRPI and SMRPI method is given by applying on mentioned problem. Convergence studies in the numerical examples show that the SMRPI method possesses excellent rates of convergence.

Research paper thumbnail of Exact analytical solution to the Poisson-Boltzmann equation for semiconductor devices

The European Physical Journal Plus, 2014

Research paper thumbnail of A new spectral meshless radial point interpolation (SMRPI) method: A well-behaved alternative to the meshless weak forms

Engineering Analysis with Boundary Elements, 2015

Research paper thumbnail of Analysis of Some Magnetohydrodynamic Flows of Third-Order Fluid Saturating Porous Space

Journal of Porous Media, 2015

ABSTRACT

Research paper thumbnail of On The Existence of Multiple Solutions of a Class of Third-Order Nonlinear Two-Point Boundary Value Problems

Mediterranean Journal of Mathematics, 2015

Research paper thumbnail of A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs

Zeitschrift für Naturforschung A, 2015

This paper presents a meshless method which, at the first step, utilises the radial basis functio... more This paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.

Research paper thumbnail of Application of the Variational Iteration Method to Nonlinear Volterra’s Integro-Differential Equations

Zeitschrift für Naturforschung A, 2008

Research paper thumbnail of Chapter 2: Predictor Homotopy Analysis Method (PHAM)

Advances in the Homotopy Analysis Method, 2013

Research paper thumbnail of Bio-inspired computing platform for reliable solution of Bratu-type equations arising in the modeling of electrically conducting solids

Applied Mathematical Modelling, 2016

Research paper thumbnail of Reliable numerical treatment of nonlinear singular Flierl–Petviashivili equations for unbounded domain using ANN, GAs, and SQP

Applied Soft Computing, 2015

Research paper thumbnail of Accepted Manuscript Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping

Please cite this article in press as: V.R. Hosseini et al., Local radial point interpolation (MLR... more Please cite this article in press as: V.R. Hosseini et al., Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping, J. Comput. Phys. (2016), http://dx. Abstract The purpose of the current investigation is to determine numerical solution of time-fractional diffusion-wave equation with damping for Caputo's fractional derivative of order α(1 < α ≤ 2). A meshless local radial point interpolation (MLRPI) scheme based on Galerkin weak form is analyzed. The reason of choosing MLRPI approach is that it dose not require any background integrations cells, instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape. The unconditional stability and convergence with order O(τ 6−2α) are proved, where τ is time stepping. Also, Several numerical experiments are illustrated to verify theoretical analysis.

Research paper thumbnail of Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping

Journal of Computational Physics, 2016

Research paper thumbnail of Monomial geometric programming with fuzzy relation inequality constraints with max-product composition

Computers and Industrial Engineering, May 1, 2009

Research paper thumbnail of Optimization of Linear Objective Function Subject to Fuzzy Relation Inequalities Constraints with Max-Average Composition

Iranian Journal of Fuzzy Systems, 2007

ABSTRACT In this paper, the finitely many constraints of a fuzzy relation inequalities problem ar... more ABSTRACT In this paper, the finitely many constraints of a fuzzy relation inequalities problem are studied and the linear objective function on the region defined by a fuzzy max-average operator is optimized. A new simplification technique which accelerates the resolution of the problem by removing the components having no effect on the solution process is given together with an algorithm and a numerical example to illustrate the steps of the problem resolution process.

Research paper thumbnail of Solution of singular linear vibrational BVPs by the homotopy analysis method

ABSTRACT In this paper, the homotopy analysis method (HAM) which is a powerful technique of nonli... more ABSTRACT In this paper, the homotopy analysis method (HAM) which is a powerful technique of nonlinear analysis, is examined in the solution of the linear vibration equation for very a large circular membrane. The method is shown to be able to handle a variety of pertaining singular boundary value problems (BVPs), to allow for graphical presentation of the results, and appears to be a viable alternative to applicable integral transform methods.

Research paper thumbnail of sdfadfA nonlinear partial integro-differential equation arising in population dynamic via radial basis functions and theta-method

Research paper thumbnail of A nonlinear partial integro-differential equation arising in population dynamic via radial basis functions and theta-method

ABSTRACT This paper proposes a numerical method to deal with the integro-differential reaction-di... more ABSTRACT This paper proposes a numerical method to deal with the integro-differential reaction-diffusion equation. In the proposed method, the time variable is eliminated by using finite difference theta− method to enjoy the stability condition. The method benefits from collocation radial basis function method, the generallized thin plate splines (GTPS) radial basis functions are used. Therefore, it does not require any struggle to determine shape parameter. The obtained results for some numerical examples reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.

Research paper thumbnail of Meshless local Petrov–Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation

Engineering Analysis with Boundary Elements, 2015

Research paper thumbnail of Multiplicity results and closed-form solution for catalytic reaction in a flat particle

Journal of the Taiwan Institute of Chemical Engineers, 2015

Research paper thumbnail of On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations

International Journal for Numerical Methods in Engineering, 2015

Research paper thumbnail of Analysis of meshless local and spectral meshless radial point interpolation (MLRPI and SMRPI) on 3-D nonlinear wave equations

Ocean Engineering, 2014

ABSTRACT In this paper, the meshless local radial point interpolation (MLRPI) method is applied t... more ABSTRACT In this paper, the meshless local radial point interpolation (MLRPI) method is applied to simulate three space dimensional nonlinear wave equation of the form utt+αut+βu=uxx+uyy+uzz+δg(u)ut+f(x,y,z,t)utt+αut+βu=uxx+uyy+uzz+δg(u)ut+f(x,y,z,t), 0&lt;x,y,z&lt;1,t&gt;0 subject to given appropriate initial and Dirichlet boundary conditions and then a new spectral meshless radial point interpolation (SMRPI) method is proposed to solve the mentioned problem. The main drawback of methods in fully 3-D problems is the large computational costs. In the MLRPI method, all integrations are carried out locally over small quadrature domains of regular shapes such as spheres or cubes. In innovative SMRPI method, it is not needed to any integration. The radial point interpolation method is proposed to construct shape functions for MLRPI and basis functions for SMRPI. A weak formulation with a Heaviside step function transforms the set of governing equations into local integral equations on local subdomains in MLRPI whereas the operational matrices converts easily the governing equations (even high order) into linear system of equations in SMRPI. A two-step time discretization method is employed to approximate the time derivatives. To treat the nonlinearity part, a kind of predictor–corrector scheme combined with one-step time discretization and Crank–Nicolson technique is adopted. A comparison study of the efficiency and accuracy of the MLRPI and SMRPI method is given by applying on mentioned problem. Convergence studies in the numerical examples show that the SMRPI method possesses excellent rates of convergence.

Research paper thumbnail of Exact analytical solution to the Poisson-Boltzmann equation for semiconductor devices

The European Physical Journal Plus, 2014

Research paper thumbnail of A new spectral meshless radial point interpolation (SMRPI) method: A well-behaved alternative to the meshless weak forms

Engineering Analysis with Boundary Elements, 2015

Research paper thumbnail of Analysis of Some Magnetohydrodynamic Flows of Third-Order Fluid Saturating Porous Space

Journal of Porous Media, 2015

ABSTRACT