Related papers: On the variational homotopy perturbation method fo…
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically…
In this paper, we present an adaptive step-size homotopy tracking method for computing bifurcation points of nonlinear systems. There are four components in this new method: 1) an adaptive tracking technique is developed near bifurcation…
We present an alternative pathway in the application of the variation improvement of ordinary perturbation theory exposed in [1] which can preserve the internal symmetries of a model by means of a time compactification.
In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…
We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation…
In this paper, we develop a drift homotopy implicit particle filter method. The methodology of our approach is to adopt the concept of drift homotopy in the resampling procedure of the particle filter method for solving the nonlinear…
In this article we study a coupled system of differential equations with Allen-Cahn type non-linearity. Motivated by physical phenomena one of the unknowns in the system is accompanied by a singular perturbation parameter ${\epsilon}^2$ .…
Far as we know there are not exact solutions to the equation of motion for a relativistic harmonic oscillator. In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is studied by…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives…
A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of…
In this paper, the fractional-order Burgers-Poisson equation is introduced by replacing the first-order time derivative by fractional derivative of order $\alpha$. Both exact and approximate explicit solutions are obtained by employing…
An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical method is an elegant combination of the Natural Transform Method (NTM) and a well-known method,…
In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…
The oscillatory behavior of the solutions to a differential equation with several non-monotone delay arguments and non-negative coefficients is studied. A new sufficient oscillation condition, involving lim sup, is obtained. An example…