Journal Cover International Journal of Mathematical Modelling & Computations
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  This is an Open Access Journal Open Access journal
   ISSN (Print) 2228-6225 - ISSN (Online) 2228-6233
   Published by Islamic Azad University Homepage  [18 journals]
  • A regularization method for solving a nonlinear backward inverse heat
           conduction problem using ...

    • Abstract: The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and convergence of the aforementioned algorithm is provided. Finally, the results of this paper have been illustrated by some numerical examples.
      PubDate: Thu, 09 Nov 2017 20:30:00 +010
  • Convection in a Tilted Square Enclosure with Various Boundary Conditions
           and Having Heat ...

    • Abstract: In this study free convection flow and heat transfer of a fluid inside a tilted square enclosure having heat conducting and generating solid body positioned in the center of the enclosure with various thermal boundary conditions has been investigated numerically. The governing equations are transformed into non-dimensional form and the resulting partial differential equations are solved by Finite Volume Method applying power-law scheme using SIMPLE algorithm with Under-Relaxation technique. The parameters leading the problem are the aspect ratio, thermal conductivity ratio, temperature difference ratio and the angle of inclination. The effect of different thermal boundary conditions on streamlines and isotherms as well as on the rate of heat transfer on all walls of the enclosure are presented graphically.
      PubDate: Mon, 06 Nov 2017 20:30:00 +010
  • Airy equation with memory involvement via Liouville differential operator

    • Abstract: In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration to the approximation and asymptotic behavior of the integral solution to the left FADE with respect to the existing parameters is presented.
      PubDate: Fri, 03 Nov 2017 20:30:00 +010
  • Dynamics of Food Chain Model: Role of Alternative Resource for Top

    • Abstract: In this paper, effect of alternative resource for top predator in food chain model with holling type III functional response is seen . Proposed model is demonstrated in respect of analytical as well numerical results. Bifurcation study with the variation of alternative resource and half saturation constants are done numerically. Simulation results shows that suitable alternative resource has the capability to prevent top predator extinction.
      PubDate: Fri, 03 Nov 2017 20:30:00 +010
  • A Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems
           of Nonlinear Equations

    • Abstract: Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear equations by incoporating the hyperplane projection and Powel restart approach. We prove the global convergence of the proposed method with a derivative free line search under suitable assumtions. the numerical results are presented which show that the proposed method is promising.
      PubDate: Fri, 03 Nov 2017 20:30:00 +010
  • On a modi cation of the Chebyshev collocation method for solving
           fractional diff usion equation

    • Abstract: In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency of the proposed method.
      PubDate: Fri, 03 Nov 2017 20:30:00 +010
  • Jacobi Operational Matrix Approach for Solving Systems of Linear and
           Nonlinear ...

    • Abstract: ‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations‎. ‎ Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. ‎The method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equations‎. ‎Illustrative examples are included to demonstrate the validity and efficiency of the presented method‎. It is further found that the absolute errors are almost constant in the studied interval. ‎Also‎, ‎several theorems related to the convergence of the proposed method‎, ‎will be presented‎‎.‎
      PubDate: Tue, 31 Oct 2017 20:30:00 +010
  • Multistage Modified Sinc Method for Solving Nonlinear Dynamical Systems

    • Abstract: The sinc method is known as an ecient numerical method for solving ordinary or par-tial di erential equations but the system of di erential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical models in disease, the detailed stability analyses and numerical experiments are given on the standard within-host virus infections model.
      PubDate: Tue, 31 Oct 2017 20:30:00 +010
  • The comparison of two high-order semi-discrete central schemes for solving
           hyperbolic ...

    • Abstract: This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux and the third-order TVD Runge-Kutta method. Also this paper compares the numerical results of these two methods. Afterwards, we are interested in the behavior of the total variation (TV) of the approximate solution obtained with these schemes. We test these schemes on both scalar and gas dynamics problems. Numerical results con rm that the new schemes are non-oscillatory and yield sharp results when solving profi les with discontinuities. We also observe that the total variation of computed solutions is close to the total variation of the exact solution or a reference solution.
      PubDate: Tue, 31 Oct 2017 20:30:00 +010
  • Influence of an external magnetic field on the peristaltic flow of a
           couple stress fluid ...

    • Abstract: Magnetohydrodynamic(MHD) peristaltic flow of a Couple Stress Fluid through a permeable channel is examined in this investigation. The flow analysis is performed in the presence of an External Magnetic Field. Long wavelength and low Reynolds number approach is implemented. Mathematical expressions of axial velocity, pressure gradient and volume flow rate are obtained. Pressure rise, frictional force and pumping phenomenon are portrayed and symbolized graphically. The elemental characteristics of this analysis is a complete interpretation of the influence of Couple Stress Parameter, magnetic number, non dimensional amplitude ratio and permeability parameter on the velocity, pressure gradient, pressure rise and frictional forces.
      PubDate: Tue, 31 Oct 2017 20:30:00 +010
  • Using Chebyshev polynomial’s zeros as point grid for numerical solution
           of nonlinear PDEs by ...

    • Abstract: Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are applied to find the numerical solution of the linear and nonlinear PDEs. The multiquadric (MQ) RBFs as basis function will introduce and applied to discretize PDEs. Differential quadrature will introduce briefly and then we obtain the numerical solution of the PDEs. DQ is a numerical method for approximate and discretized partial derivatives of solution function. The key idea in DQ method is that any derivatives of unknown solution function at a mesh point can be approximated by weighted linear sum of all the functional values along a mesh line.
      PubDate: Tue, 31 Oct 2017 20:30:00 +010
  • Approximate solution of system of nonlinear Volterra integro-differential
           equations by using ...

    • Abstract: This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the given conditions, to a system of nonlinear algebraic equations. By solving such arising non linear system, the Bernstein coefficients can be determined to obtain the finite Bernstein series approach. Numerical examples are tested and the resultes are incorporated to demonstrate the validity and applicability of the approach. Comparisons with a number of conventional methods are made in order to verify the nature of accuracy and the applicability of the proposed approach. Keywords: Systems of nonlinear Volterra integro-differential equations; The Bernstein polyno- mials and series; Collocation points. 2010 AMS Subject Classi cation: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20.
      PubDate: Tue, 31 Oct 2017 20:30:00 +010
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