Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/21258
Title: Study of Evolutionary Computational Paradigm for Solving Nonlinear Systems of Differential Equations
Authors: Ali, Sharafat
Keywords: Physical Sciences
Mathematics
Issue Date: 2022
Publisher: University of Gujrat, Gujrat
Abstract: An integrated deterministic stochastic numerical computing solver is presented for numerical treatment of some ordinary di erential equations (ODEs). Firstly, this novel technique is tested for the dynamical investigation of nano uidic problem with Williamson uid ow on a stretching sheet by considering the thermal slip and velocity. The impact of thermophoresis and Brownian motion on phenomena of heat transfer are explored by using Buongiorno model. The governing non-linear partial di erential system representing the mathematical model of the Williamson uid is transformed in to a system of ODEs by incorporating the competency of non-dimensional similarity variables. The dynamics of the transformed system of ODEs are evaluated through the designed method. Su cient graphical and numerical illustrations are portrayed in order to investigate and analyze the in uence of physical parameters. The numerically computed values of local Nusselt number, local Sherwood number, and skin friction coe cient are also inspected for exhaustive assessment. Secondly, the designed numerical computing solver extended and developed an innovative bio-inspired algorithm based on evolutionary cubic splines method (ECSM). This integrated computational intelligent solver has been utilized to estimate the numerical results of nonlinear ordinary di erential equations (NODEs) such as Painlev e-I, Painlev e-IV, Painlev e-VI, Bratu and Troesch's problems. The design solver ECSM transforms the NODEs into nonlinear system of equations and its tness function is developed on mean square error sense. The computational mechanism is used to support the design solver ECSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick re nement. In this process variation of splines is implemented for various scenarios. The ECSM develops an interpolated function that is continuous up to its second derivative. The design solver provides a reliable and excellent procedure to obtain the unknown coe cients of splines and optimized the results. The results obtained from multiple independent runs with negligible absolute error reveal that the proposed scheme is e ective in terms of accuracy and convergence to solve NODEs. The e ciency of designed scheme is additionally endorsed through statistical assessments on measures of central tendency and variation via mean, standard deviation, minimum and maximum values of residual errors.
Gov't Doc #: 27096
URI: http://prr.hec.gov.pk/jspui/handle/123456789/21258
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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