Abstract The neural ordinary differential equation (neural ODE) is a novel machine learning architecture whose weights are smooth functions of the continuous depth. We apply ODE to holographic QCD by regarding weight as bulk metric, and train with lattice data chiral condensate at finite temperature. finds consistent geometry various values temperature discovers emergent black hole horizon in a...

In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

tension-leg platform (tlp) is a vertically moored floating structure. the platform is permanently mooredby tendons. surge equation of motion of tlp is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. this paper compare the dynamic motion responses of a tlp in regular sea waves obtained by applying three method in time domain usin...

Further extension of the generalized and improved (G0/G)-expansion method; Nonlinear ordinary differential equation; ZKBBM equation; Travelling wave solutions Abstract In this article, the generalized and improved (G0/G)-expansion method has been proposed for further extension to generate many new travelling wave solutions. In addition, nonlinear ordinary differential equation is implemented as...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

In this paper we introduce a new method for solving partial and ordinary differential equations with large first, second and third derivatives of the solution in some part of the domain using the finite element technique (here called the Galerkin-Gokhman method). The method is based on the application of the Galerkin method to a modified differential equation. The exact solution of the modified...