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Meta-heuristic algorithms for solving nonlinear differential equations based on multivariate Bernstein polynomials
Faculty
Science
Year:
2021
Type of Publication:
ZU Hosted
Pages:
605–619
Authors:
Rasha Mohamed AbuBakr AbedRabbo
Staff Zu Site
Abstract In Staff Site
Journal:
Soft Computing Germany, part of Springer Nature
Volume:
26
Keywords :
Meta-heuristic algorithms , solving nonlinear differential equations based
Abstract:
This paper concerns with solving nonlinear boundary value problems with Dirichlet boundary conditions by a novel approximation technique based on Bernstein polynomials and meta-heuristic algorithms. A trial solution is expressed as a weighted sum of Bernstein polynomials of degree n. Some weights of this trial solution are determined by enforcing exact satisfaction of the Dirichlet boundary conditions. The remaining weights are determined such that they minimize the sum of squares of the residuals of the differential equation computed at arbitrary set of interior points in the domain of the problem. Error bounds for the approximate solutions for ordinary and partial differential equations are derived. The resulting optimization problem is solved using meta-heuristic algorithms, namely particle swarm optimization (PSO), genetic algorithm (GA), and a hybrid PSO–GA algorithm. The accuracy of the proposed approach is demonstrated by solving some nonlinear boundary value problems including Bratu problems in one- and two-dimensional spaces
Author Related Publications
Rasha Mohamed AbuBakr AbedRabbo, "Multi-objective optimization for lightweight design of bi-directional functionally graded beams for maximum frequency and buckling load", Elsevier, 2021
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Rasha Mohamed AbuBakr AbedRabbo, "Weight optimization of axially functionally graded microbeams under buckling and vibration behaviors", Taylor & Francis Group, 2020
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Department Related Publications
Salwa Amien Mohamed ebrhiem, "Adaptive FAS-Multigrid Method for Nonlinear Elliptic Equations on Unstructured Grids", لايوجد, 1900
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Amr Mohamed Salaheldeen Abdelaziem Mohamed, "Evaluation o Green's unction derivatives or exponentially graded elasticity", لايوجد, 1900
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Salwa Amien Mohamed ebrhiem, "Optimally efficient multigrid algorithms for incompressible Euler equations", Emerald Group Publishing Limited, 2008
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Salwa Amien Mohamed ebrhiem, "Adaptive FAS-multigrid method for nonlinear elliptic equations on unstructured grids", Wiley InterScience, 2007
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Rania Bahgat Mohamed Amer, "An Efficient Method To Solve Thermal Wave Equations", Published by Scientific Research Publishing, 2014
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