Browse Articles

    Volume 2, Issue 2, March 2016

    An approximate analytical solution approach for solving time-Fractional order Black-Scholes Option pricing equation
    B.K. Singh, P. Kumar, V. Kumar
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      • Abstract: The present article is concerned the implementation of fractional-order reduced differential transform (FRDT) method for computation of an approximate analytical solution of time-fractional order nonlinear Black-Scholes option pricing equation, fractional derivative is considered in the Caputo sense. Three test examples are carried out to validate and illustrate the efficiency of the method. The computational examples confirm that the aforesaid method is very effective, reliable and accurate method for solving the nonlinear Black-Scholes equation. The behaviour of the solutions and effects of different values of fractional order are also depicted, graphically.

    Optimal harvesting of a ratio-dependent predator-prey model with strong Allee effect
    M.K. Singh, B.S. Bhadauria, B.K. Singh
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      • Abstract: In the present paper, we propose a ratio-dependent predator-prey model with strong Allee effect in the presence of linear harvesting in both the prey and the predator species. The equilibria of the model are obtained and their stability is discussed. By taking the harvesting parameter as bifurcation parameter, we discuss the saddle-node bifurcation, and hence the harvesting rate for the maximum sustainable yields (MSY). We find the condition under which the bionomic equilibria exist. By using the Pontryagin's maximum principle, we have derived singular optimal control for the associated control problem. Numerical simulations have been carried out to validate the analytical findings.

    Digital image quality measurements
    V.K. Mishra, S. kumar , S. Singh
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      • Abstract: In the present scenario human life become very fast. In such a dynamic environment people have no time for each other, even though we want to capture each and every moment of our life for future perspective. There are multiple electronic gadgets in the market by means of which we can capture pictures to remember the golden moments. In the age of social networking everybody wants to keep themselves updated by means of image, selfies and pictures so it is the need of time to discuss about the quality of picture and the way to enhance and create better pictures.

    Numerical computation of Klein-Gordon equation by two methods
    B.K. Singh
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      • Abstract: This paper deals with a comparative study of as approximate numerical solution of Klein-Gordon (KG) equation obtained by modified cubic B-spline differential quadrature method and fourth-order compact finite difference scheme. The numerical solutions of the equation are included to confirm the efficiency and accuracy of these methods. The comparison between these two schemes by means of the maximum errors and error norms of three test problems are presented.

    Melting-solidification characteristics of phase change materials in two macro encapsulations for development of thermal energy storage system for a solar timber drying kiln
    S. Kumar, V.S.K. Kumar
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      • Abstract: A prototype of semi green house type solar dryer of 1m3 capacity was used in the study. In order to develop efficient latent heat based thermal energy storage system (TESS), combinations of two macro-encapsulations (container) with two phase change materials (PCM) were studied. Two organic PCM i.e. fatty acid mixture and paraffin were used to study their melting and solidification properties in two types of container materials: high density poly ethylene (HDPE) and aluminium. The melting- solidification studies were made in actual working conditions of the system i.e. packed bed active TESS (water as media) and passive TESS (air as media). The results suggest that container properties influence melting of two PCMs. Higher thermal conductive container helps to melt PCM faster. Solidification of PCM was not found to be affected by container property. Melting occurred faster when water was taken as heat transfer medium..

    Numerical simulation of three dimensional advection-diffusion equations by using modified cubic B-spline differential quadrature method
    M. Tamsir, V.K. Srivastava, P.D. Mishra
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      • Abstract: In this paper, modified cubic B-spline differential quadrature method is proposed to solve the three dimensional advection-diffusion equations, subjected to appropriate initial and boundary conditions. This method is basically differential quadrature method where the weighting coefficients are computed by taking the modified cubic B-splines functions as basis functions. This method transforms the advection-diffusion equations into a system of first-order ordinary differential equations (ODEs). SSP-RK54 scheme is applied to solve the resulting system of first order ODEs. The proposed MCB-DQM is unconditionally stable for advection-diffusion equations. The accuracy and efficiency of MCB-DQM is illustrated by two test problems. It is evident that the solutions obtained by the proposed method are in good agreement with the exact solutions..