Heuristic computational intelligence approach to solve nonlinear multiple singularity problem of sixth Painlev́e equation

Abstract

The present study investigate the numerical solution of nonlinear singular system represented with sixth Painleve equation by the strength of artificial intelligence using feed-forward artificial neural networks (ANNs) optimized with genetic algorithms (GAs), interior point technique (IPT), sequential quadratic programming (SQP), and their hybrids. The ANN provided a compatible method for finding nature-inspired mathematical model based on unsupervised error for sixth Painleve equation and adaptation of weights of these networks is carried out globally by the competency of GA aided with IPT or SQP algorithms. Moreover, a hybrid approach has been adopted for better proposed numerical results. An extensive statistical analysis has been performed through several independent runs of algorithms to validate the accuracy, convergence, and exactness of the proposed scheme.

A design of novel Gudermannian neural networks for the nonlinear multi-pantograph delay differential singular model

“…The multi-pantograph delay differential (MP-DD) involving multiple singularities always difficult, grim, and challenging to solve numerically [1,2]. The MP-DD equations arise in various fields of applied physics and technology, such as astrophysics [3], electrodynamics [4], nonlinear dynamical models [5], electronic models [6], Hamiltonian systems [7], multimodal human computer interaction [8], catenary system [9], complex plane [10] and the problems related to engineering physics [11][12][13]. There are many powerful numerical techniques available in the literature to find the approximate results of the MP-DD equations.…”

Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming

“…Few potential applications of SS for solution of differential equations include nonlinear optics studies [17], applications of random matrix theory [18], nonlinear stiff oscillatory systems based on Van der Pol oscillator [19], fuzzy nonlinear systems [20], magnetohydrodynamic problems [21], inverse kinematics problem [22], nonlinear Jeffery-Hamel flow model [23], parameter estimation [24], fuel ignition systems [25], fuzzy Fredholm-Volterra integrodifferential equations [26], nonlinear drainage problem based on Johnson-Segalman fluid [27], electrical conducting solids [28], nonlinear problems arising in nanotechnology [29], astrophysics [30], plasma physics [31], atomic physics [32], model of heartbeat dynamics [33], models of HIV infection of CD4+ T-cell model [34], fractional order systems [35], economic [36] and finance [37]. Additionally, analysis of nonlinear systems based on Thomas-Fermi [38], Lane-Emden [29], Emden-Fowler [40], Bratu [41], Troesch [42], Riccati [43], Flierl-Petviashivili [44], Beglay-Torviq [45], Pantograph [46], Van der Pol [47] and Painlevé type equations [48] are other illustrative application of stochastics solvers. The competency of these methodologies to nonlinear problem arising in circuit theory can play a fundamental role due to unavailability of exact solution and strong nonlinearity in the governing mathematical models.…”