Some notes on the general boundary element method for highly nonlinear problems

Wu, Yuze; Liao, Shijun; Zhao, Xiaohui

doi:10.1016/j.cnsns.2004.04.003

Cited by 9 publications

(2 citation statements)

References 44 publications

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“…Some valuable results for solving different nonlinear equations have recently been obtained. There are several analytical methods that refer to nonlinear problems, such as the weighted linearization process [7], Lindstedt-Poincare method [8], Adomian decomposition technique [9], boundary element technique [9], optimal perturbation homotopy method [10], optimal asymptotic homotopy method [11], etc. [12].…”

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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Section: Introductionmentioning

confidence: 99%

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

2021

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“…Gabriella used extrapolation spaces to solve Banach spaces valued delay differential equations with unbounded delay operators. The author proved regularity properties of various types of solutions and investigated the existence of strong and weak solutions for a class of abstract semilinear delay equations 17 . In this paper, finite difference see, e.g., 18-28 and homotopy analysis methods HAM see, e.g., [29][30][31][32][33][34][35][36][37] Difference schemes which are accurate to first and second orders for the approximate solution of problem 1.1 are presented. The convergence estimates for the solution of these difference schemes are obtained.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition

Agirseven

2012

Abstract and Applied Analysis

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Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. A procedure of modified Gauss elimination method is used for the solution of these difference schemes. Homotopy analysis method is applied. Comparison of finite difference and homotopy analysis methods is given on the problem.

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