An Efficient Algorithm based on the Cubic Spline for the Solution of Bratu-Type Equation

Al-Towaiq, Mohammad H.; Ala’yed, Osama

doi:10.1080/09720502.2013.842050

Cited by 7 publications

(1 citation statement)

References 10 publications

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“…Moreover, research community is interested in splines method to solve different types of differential equations in wide scale. Some examples of such approach are given in [49][50][51][52][53][54][55]. Recently, the spline method has been considered by the researchers as an ideal numerical method for solving many problems.…”

Section: Introductionmentioning

confidence: 99%

Design of Spline–Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model

2021

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A novel design of stochastic numerical computing method is introduced for computational fluid dynamics problem governed with nonlinear thin film flow (TFF) system by exploiting the competency of polynomial splines for discretization and optimization with evolutionary computing aided with brilliance of local search. The TFF model of second grade fluid is represented with nonlinear second-order differential system. The aim of the present work is to exploit the cubic spline approach (CSA) to transform the differential equations for TFF model into an equivalent set of nonlinear equations. The approximation in mean squared error sense is introduced for the formulation of cost function for solving the nonlinear system of equations representing TFF model. The optimization of the decision variables of the cost function is carried out with global search efficacy of evolution by genetic algorithms (GAs) integrated with sequential quadratic programming (SQP) for speedy adjustments. The designed spline-evolutionary computing paradigm, CSA-GA-SQP, is evaluated for different scenarios of TFF model by variation of second grade and magnetic parameters, as well as variation in the length of splines. Results endorsed the worth of CSA-GA-SQP solver as an efficient alternative, reliable, stable, and accurate framework for the variants of nonlinear TFF systems on the basis of multiple autonomous executions. The design computing spline paradigm CSA-GA-SQP is a promising alternative numerical solver to be implemented for the solution of stiff nonlinear systems representing the complex scenarios of computational fluid dynamics problems.

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