in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

We present an adaptive animation method for electrical discharges. Electric discharges can be simulated using the dielectric breakdown model. Regular discretization of the governing Laplace equation leads to huge equation systems, and the computational cost of solving the equations quickly becomes prohibitive at high resolutions, especially for simulations in 3D. In contrast, our method discret...

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...

In this paper we study intermittency for the parabolic Anderson equation ∂u/∂t = κ∆u + ξu, where u : Z d × [0, ∞) → R, κ is the diffusion constant, ∆ is the discrete Laplacian, and ξ : Z d × [0, ∞) → R is a space-time random medium. We focus on the case where ξ is γ times the random medium that is obtained by running independent simple random walks with diffusion constant ρ starting from a Pois...

The generalized coupled thermo-viscoelasticity of hollow sphere subjected to thermal symmetric shock load is presented in this paper. To overcome the infinite speed of thermal wave propagation, the Lord-Shulman theory is considered. Two coupled equations, namely, the radial equation of motion and the energy equation of a hollow sphere are obtained in dimensionless form. Resulting equations are ...

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

In this paper, we develop new methods of solving the Poincaré-Lelong equation. It is mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1)-forms. The method is shown to be effective through obtaining better, sometimes optimal, existence results for the Poincaré-Lelong equation.