in this work, we study the performance of the sinc-collocation method for solving bratu's problem. for different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. the comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with

In this article, we discuss the numerical solution of Bingham-Bratu-Gelfand (BBG) problem, a non-smooth nonlinear eigenvalue problem associated with total variation integral and an exponential nonlinearity. Using fact that one can view as possible Lagrange multiplier constrained minimization from Calculus Variations, associate BBG initial value (dynamical flow), well suited to time-discretizati...

Abstract We address a new numerical method based on class of machine learning methods, the so-called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for computation steady-state solutions construction (one-dimensional) bifurcation diagrams nonlinear partial differential equations (PDEs). For our illustrations, we considered two benchmark problems, namely (a) one-...

in this paper, the homotopy perturbation method (hpm) is applied to obtain an approximate solution of the fractional bratu-type equations. the convergence of the method is also studied. the fractional derivatives are described in the modied riemann-liouville sense. the results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional...

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

In this paper we establish existence and multiplicity results for a class of fully nonlinear elliptic equations of k-Hessian type with exponential nonlinearity. In particular, we characterize the precise dependence of the multiplicity of solutions with respect to both the space dimension and the value of k. The choice of exponential nonlinearity is motivated by the classical Liouville-Gelfand p...

where λ is a spectral parameter, Y (x) = [yk(x)]k=1,d is a column vector, Q(x) and M(x, t) are d×d real symmetric matrix-valued functions, and h and H are d×d real symmetric constant matrices. M(x, t) is an integrable function on the set D0 def ={(x, t) : 0≤ t ≤ x ≤ π, x, t ∈ R}, Q ∈ C1[0,π], where C1[0,π] denotes a set whose element is a continuously differentiable function on [0,π]. In partic...

We provide Harish-Chandra type formulas for the multivariate Bessel functions and HeckmanOpdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof-Kirillov Jr. in [EK94]. Integration over the Liouville tori of the Gelf...

In this work, we study the performance of the sinc-Collocation method for solving Bratu's problem. For different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. The comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with