small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. non-fourier heat transfer overcomes some shortcomings of fourier heat tran...

in this paper we consider the european continuous installment call option. then  its linear complementarity formulation is given. writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. finally finite element method is applied to price the european continuous installment call option.

Variational integrators are symplectic-momentum preserving integrators that are based on a discrete variational formulation of the underlying system. So far, variational integrators have been mainly developed and used for a wide variety of mechanical systems. In this work, we develop a variational integrator for the simulation of electric circuits. An appropriate variational formulation is pres...

This work presents an alternative formulation of resolvent analysis based on the calculus variations. The proposed circumvents reliance inversion linear operator and is inherently compatible with any arbitrary choice norm. Several examples are presented which highlight analytical numerical advantages limitations formulation.

This work presents a novel approach to well established concepts of gravity, formulating new and consistent gravitoelectromagnetic theory. The long standing field theory is considered in the framework Hamilton’s principle. A variational formulation based on this principle describes dynamics fully-relativistic perfect fluid presence flat space, leading definition energy-momentum tensors. relativ...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

In this work we present a variational formulation for neural networks. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for neural networks provides a direct method for the solution of general variational problems, in any dimension and up to any degr...

Variational inequalities have found many applications in applied science. A partial list includes obstacles problems, fluid flow in porous media, management science, traffic network, and financial equilibrium problems. However, solving variational inequalities remain a challenging task as they are often subject to some set of complex constraints, for example the obstacle problem. Domain decompo...