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2019, Volume 20, Issue 10

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Frontiers of Information Technology & Electronic Engineering >> 2019, Volume 20, Issue 10 doi: 10.1631/FITEE.1900221

Differential evolution based computation intelligence solver for elliptic partial differential equations

Affiliation(s): Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad 45650, Pakistan; Department of Computer and Information Sciences, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad 45650, Pakistan; Department of Physics and Applied Mathematics, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad 45650, Pakistan; School of Electrical and Electronic Engineering, University of Adelaide, Adelaide 5005, Australia; Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan; less

Accepted: 2019-11-11 Available online: 2019-11-11
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Abstract

A based methodology is introduced for the solution of elliptic s (PDEs) with Dirichlet and/or Neumann boundary conditions. The solutions evolve over bounded domains throughout the interior nodes by minimization of nodal deviations among the population. The elliptic PDEs are replaced by the corresponding system of finite difference approximation, yielding an expression for nodal residues. The global residue is declared as the root-mean-square value of the nodal residues and taken as the cost function. The standard is then used for the solution of elliptic PDEs by conversion to a minimization problem of the global residue. A set of benchmark problems consisting of both linear and nonlinear elliptic PDEs has been considered for validation, proving the effectiveness of the proposed algorithm. To demonstrate its robustness, sensitivity analysis has been carried out for various operators and parameters. Comparison of the based computed nodal values with the corresponding data obtained using the exact analytical expressions shows the accuracy and convergence of the proposed methodology.

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