The Experts below are selected from a list of 2805 Experts worldwide ranked by ideXlab platform

Marius Ghergu - One of the best experts on this subject based on the ideXlab platform.

Vicenţiu D Rădulescu - One of the best experts on this subject based on the ideXlab platform.

Vicentiu Radulescu - One of the best experts on this subject based on the ideXlab platform.

Muhammad Asif Zahoor Raja - One of the best experts on this subject based on the ideXlab platform.

  • Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler Equation
    Computational and Applied Mathematics, 2020
    Co-Authors: Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Juan L. G. Guirao, Muhammad Shoaib
    Abstract:

    In the present work, a novel neuro-swarming based heuristic solver is established for the numerical solutions of fourth-order multi-singular nonlinear Emden–Fowler (FO-MS-NEF) model using the function estimate capability of artificial neural networks (ANNs) modelling together with the global application of particle swarm optimization (PSO) enhanced by local search active set (AS) approach, i.e., ANN-PSO-AS solver. The design stimulation for the ANN-PSO-AS scheme for a numerical solver originates with an intention to present a viable, consistent and precise configuration that associates the ANNs strength under the optimization of unified soft computing backgrounds to tackle with such stimulating models for the FO-MS-NEF Equation. The proposed ANN-PSO-AS solver is applied for three different variants of FO-MS-NEF Equations. The comparison of the obtained results with the true solutions calmed its correctness, effectiveness, and robustness that is further validated with in-depth statistical investigations.

  • Integrated intelligent computing paradigm for nonlinear multi-singular third-order Emden–Fowler Equation
    Neural Computing and Applications, 2020
    Co-Authors: Zulqurnain Sabir, Muhammad Umar, Juan L. G. Guirao, Muhammad Shoaib, Muhammad Asif Zahoor Raja
    Abstract:

    In this study, an advance computational intelligence scheme is designed and implemented to solve third-order nonlinear multiple singular systems represented with Emden–Fowler differential Equation (EFDE) by exploiting the efficacy of artificial neural networks (ANNs), genetic algorithms (GAs) and active-set algorithm (ASA), i.e., ANN–GA–ASA. In the scheme, ANNs are used to discretize the EFDE for formulation of mean squared error-based fitness function. The optimization task for ANN models of nonlinear multi-singular system is performed by integrated competency GA and ASA. The efficiency of the designed ANN–GA–ASA is examined by solving five different variants of the singular model to check the effectiveness, reliability and significance. The statistical investigations are also performed to authenticate the precision, accuracy and convergence.

  • Numerical treatment of nonlinear Emden–Fowler Equation using stochastic technique
    Annals of Mathematics and Artificial Intelligence, 2011
    Co-Authors: Junaid Ali Khan, Muhammad Asif Zahoor Raja, Ijaz Mansoor Qureshi
    Abstract:

    The article is based on the approximate solution of a well known Lane–Emden–Fowler (LEF) Equation. A trial solution of the model is formulated as an artificial feed-forward neural network containing unknown weights which are optimized in an unsupervised way. The proposed scheme is tested successfully on various test cases of initial value problems of LEF Equations. The reliability and effectiveness is validated through comprehensive statistical analysis.

Tobias Weth - One of the best experts on this subject based on the ideXlab platform.

  • n vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh poisson and the lane emden fowler Equations
    Communications in Mathematical Physics, 2010
    Co-Authors: Thomas Bartsch, Angela Pistoia, Tobias Weth
    Abstract:

    We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain \({\Omega\subset\mathbb{R}^2}\) , which is not necessarily simply connected. On an arbitrary bounded domain we obtain new equilibria for N = 3 or N = 4. If Ω has an axial symmetry we obtain a symmetric equilibrium for each \({N\in\mathbb{N}}\) . We also obtain new stream functions solving the sinh-Poisson Equation \({-\Delta\psi=\rho\sinh\psi}\) in Ω with Dirichlet boundary conditions for ρ > 0 small. The stream function \({\psi_\rho}\) induces a stationary velocity field \({v_\rho}\) solving the Euler Equation in Ω. On an arbitrary bounded domain we obtain velocitiy fields having three or four counter-rotating vortices. If Ω has an axial symmetry we obtain for each N a velocity field \({v_\rho}\) that has a chain of N counter-rotating vortices, analogous to the Mallier-Maslowe row of counter-rotating vortices in the plane. Our methods also yield new nodal solutions for other semilinear Dirichlet problems, in particular for the Lane-Emden-Fowler Equation \({-\Delta u=|u|^{p-1}u}\) in Ω with p large.