Department of Mathematics

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https://escholar.umt.edu.pk/handle/123456789/348

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Browsing Department of Mathematics by Author "A. Sana"

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    Analysis of stability and accuracy for forward time centered space approximation by using modified equation
    (Science International, 2015) Tahir Ch; N.A. Shahid; M.F. Tabassum; A. Sana; S.Nazir
    In this paper we investigate the quantitative behavior of a wide range of numerical methods for solving linear partial differential equations [PDE’s]. In order to study the properties of the numerical solutions, such as accuracy, consistency, and stability, we use the method of modified equation, which is an effective approach.To determine the necessary and sufficient conditions for computing the stability, we use a truncated version of modified equation which helps us in a better way to look into the nature of dispersive as well as dissipative errors. The heat equation with Drichlet Boundary Conditions can serve as a model for heat conduction, soil consolidation, ground water flow etc.Accuracy and Stability of Forward Time Centered Space (FTCS) scheme is checked by using Modified Differential Equation [MDE].
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    Minimization of two bar bracket optimization problem through derivative free methods
    (Science International, 2015) Sadaf, S.; M. F. Tabassum; A. Sana; N. A. Shahid; N. A. Chaudhry; M. Saeed
    The purpose of this exploration is to construct optimization models of two bar bracket alongside stress constraints. The derivative free methods Nelder-Meed Method, Hooke-Jeeve Method and Multidirectional Search Methods are used to solve model. Penalty functions are used to eliminate constraints. Then constrained optimization model is changed into unconstrained model. Finally discuss the comparison and efficiency of these methods through MATLAB Programming.