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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
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  • On a modi cation of the Chebyshev collocation method for solving
           fractional diffiusion 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: Tue, 31 Oct 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: Tue, 31 Oct 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: Tue, 31 Oct 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: Tue, 31 Oct 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: Tue, 31 Oct 2017 20:30:00 +010
  • 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: Tue, 31 Oct 2017 20:30:00 +010
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Heriot-Watt University
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