K. Ivaz

• Faculty Member at University of Tabriz

The purpose of this article is to give a new study to a simple one dimensional fuzzy free boundary problem of the one-phase Stefan kind for a heat partial differential equation. The design objective is to find a fuzzy solution to satisfy precisely the partial differential equation with a free boundary condition. The results are illustrated by an ex...

The initial attached cell layer in multispecies biofilm growth is studied in this paper. The corresponding mathematical model leads to discuss a free boundary problem for a system of nonlinear hyperbolic partial differential equations, where the initial biofilm thickness is equal to zero. No assumptions on initial conditions for biomass concentrati...

The initial attached cell layer in multispecies biofilm growth is studied in this paper. The corresponding mathematical model leads to discuss a free boundary problem for a system of nonlinear hyperbolic partial differential equations, where the initial biofilm thickness is equal to zero. No assumptions on initial conditions for biomass concentrati...

In this paper, we discuss the Banach fixed point theorem conditions on the optimal exercise boundary of American put option paying continuously dividend yield, to investigate whether its existence, uniqueness, and convergence are derived. In this respect, we consider the integral representation of the optimal exercise boundary which is extracted as...

In this paper, we consider illiquid European call option which is arisen in nonlinear Black-Scholes equation. In this respect, we apply the Newton's method to linearize it. Based on the obtained linear equation, we obtain the approximate solutions recursively in two steps. Finally, based on the conditions of Kantorovich theorem, we investigate the...

This paper addresses a computational technique for solving 2D unsteady Navier-Stokes equations (NSEs) with time fractional order in the Caputo sense in the formulation of stream function-vorticity. The finite difference based method of lines (MOL) is used to discretize the time-fractional NSEs on a collocated grid that construct a fractional differ...

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute e...

The main aim of this paper is to find t-best approximation in fuzzy n-normed linear space via the optimization formulation. It is formulated as a constrained minimization problem which is solved by using penalty method. Each penalty is solved by using inexact steepest descent algorithm.

This paper describes a robust, accurate and efficient scheme based on a cubic spline interpolation. The proposed scheme is applied to approximate variable-order fractional integrals and is extended to solve a class of nonlinear variable-order fractional equations with delay. Modified Hutchinson equation and delay Ikeda equation are solved using the...

This paper aims to present a detailed analysis of the free vibration of a cantilever microbeam submerged in an incompressible and frictionless fluid cavity with free boundary condition approach. In other words, in addition to the kinematic compatibility on the boundary between microbeam and its surrounding fluid, equations of the potential function...

We study dual integral equations which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions. These equations will be converted to a system of singular integral equations with Cauchy type kernels. Using Chebyshev polynomials, we propose a method to approximate the solution of Cauchy type singular...

In this paper, the dynamic response of a micro-beam immersed in a fluid with regard to the free boundary of the operating fluid is investigated. In other words, in addition to the kinematic compatibility on the boundary between micro-beam and its surrounding fluid, equations of the potential functions are modeled considering the free boundaries. It...

The main aim of this paper is to find t-best approximation in a fuzzy normed space via the optimization formulation. It is formulated as a constrained minimization problem which is solved by using penalty method. Each penalty is solved by using inexact steepest descent algorithm.

We study dual integral equations which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions. These equations will be converted to a system of singular integral equations with Cauchy type kernels. Using Chebyshev polyno-mials, we propose a method to approximate the solution of Cauchy type singula...

In this paper we consider the European continuous installment call option. Then its linear complementarity formulation is given. Writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. Finally finite element method is applied to price the European continuous installment call option. ------------...

The aim of the present work is to introduce solution of special dual integral equations by the orthogonal polynomials. We consider a system of dual integral equations with trigonometric kernels which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions and convert them to Cauchy-type singular in...

Vibration of a beam has extensive applications in engineering and industry. The objective of this article is to provide a novel analytical model by free boundary approach to derive a more exact model for the small oscillations of a cantilever microbeam in contact with an incompressible bounded fluid in a cavity. First, a system of integral equation...

In this paper, a new method of fundamental solution (MFS) without discretization for solving the vibration equation is proposed. The presented solution has two kernels of functions of spatial and time variables. The kernels contain Fresnel integrals which have some interesting properties.

The classical one-phase one-dimensional Stefan problem is a boundary value problem involving a parabolic partial-differential equation, along with two boundary conditions on a moving boundary. In Stefan problem the moving boundary s and the distribution of temperature u in the domain are unknown and must be determined. In this paper, an approximate...

Numerical algorithms for solving first-order fuzzy differential equations and hybrid fuzzy differential equations have been investigated. Sufficient conditions for stability and convergence of the proposed algorithms are given, and their applicability is illustrated with some examples.

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of t...

In this paper we proposed a multiobjective optimization model for wireless sensor networks (WSNs). The proposed model optimized several objectives, simultaneously. Indeed, by starting from a generic configuration we found new location for sensors, that the network have appropriate performance in terms of energy consumption and travelled distance. F...

In this paper we proposed a multi-objective optimization model for wireless sensor networks (WSNs). The proposed model optimized several objectives, simultaneously. Indeed, by starting from a generic configuration we found new location for sensors, that the network have appropriate performance in terms of energy consumption and travelled distance....

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the ap-proximate analytical solutions. Numerical results are given for several examples involving scala...

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

The aim of this paper is to present an efficient numerical procedure for solving the two-dimensional nonlinear Volterra integro-differential equations (2-DNVIDE) by two-dimensional differential transform method (2-DDTM). The technique that we used is the differential transform method, which is based on Taylor series expansion. Using the differentia...

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of t...

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of t...

The moving solid/liquid interface of a melting solid in the one-dimensional case is identified from temperature and flux measurements performed solely on the solid part. We devote to control which one consists of searching for the boundary conditions in order to generate a prescribed interface.

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. Then we show that any suitable numerical method for ODEs can be applied to solve numerically fuzzy di...

In this paper, some numerical procedures for solving fuzzy first-order initial value problem have been investigated. Sufficiently conditions for stability and convergence of the proposed algorithms are given and their applicability is illustrated with examples.

Higher-order fuzzy differential equations with initial value conditions are considered. We apply the new results to the particular case of second-order fuzzy linear differential equation.

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial va...

The Newton method is applied to linearize a nonlinear Fredholm integro-differential equation to obtain a linear Fredholm integro-differential equation and so the tau numerical solution of the linear form.

In this note, we study the approximate solutions of nonlinear stochastic differential equations by using the theories and methods of mathematics analysis. An approximate method based on piecewise linearazation is developed for the determination of semi-analytical-numerical solution of nonlinear stochastic differential equations. Also, linearazation...

The aim of this paper is to present an efficient analytical and numerical procedure for solving the high-order nonlinear Volterra–Fredholm integro-differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro-differential equation and the given conditions into the matrix equation. The reliabili...

Many applied problems have their natural mathematical setting as integral and integro-differential equations, thus they usually have the advantage of simpler methods of solution. In addition, a large class of initial and boundary value problems, associated with differential equations, can be reduced to integral equations. Problems in human populati...

In this paper, the Newton's method is applied to linearize a nonlinear Fredholm integral equation of the second kind and obtain a linear Fred- holm integral equation and so we found the Tau's numerical solution of the linear form.

We consider the trapezoidal rule and the spline rule and obtain the error formula for the spline rule. Finally, we compare the error of this two methods.

This paper contains a brief introduction to FarsiTeX, a document preparation tool in Farsi Language based on LATEX, as well as explaining the difficulties of spell cheking in that.

Newton’s method is applied to linearize a system of nonlinear Fredholm integral equations of second kind and obtain a system of linear Fredholm integral equations and so we found Tau’s numerical solution of the linear form.

This paper is concerned with an inverse problem involving a two-phase moving boundary in two dimensional solidification of pure substance. Using a unique continuation result due to Saut and Schcurer we prove a uniqueness result.

This paper considers a class of one-dimensional solidification problems, in which a kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed.

This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free b...

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.