Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...

We introduce new definitions of convergence, based on adding stability criteria to Γ-convergence, that are suitable in many cases for studying convergence of local minimizers.

This paper focuses on analyzing the finite-time convergence of a nonlinear consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis of the closed-loop system under the proposed consensus algorithm are more challenging than those under the...

The design of underground spaces is mainly carried out using empirical, analytical, and numerical methods. The convergence confinement method (CCM) is an analytical technique that is widely utilized in analyzing the stability of underground spaces. However, the main challenge in the stability analysis is the selection of an accurate constitutive model for rock mass, and particularly, its post-f...

Several convergence and stability issues of the balanced implicit methods (BIMs) for systems of real-valued ordinary stochastic differential equations are thoroughly discussed. These methods are linear-implicit ones, hence easily implementable and computationally more efficient than commonly known nonlinear-implicit methods. In particular, we relax the so far known convergence condition on its ...

We show in a rather general setting that Hoelder and Lipschitz stability properties of 5 solutions to variational problems can be characterized by convergence of more or less abstract iteration 6 schemes. Depending on the principle of convergence, new and intrinsic stability conditions can be 7 derived. Our most abstract models are (multi-) functions on complete metric spaces. The relevance 8 o...

in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

In this paper we report results on stability and convergence of twolevel difference schemes for parabolic interface equations. Energy norms that rely on spectral problems containing the eigenvalue in boundary conditions or in conditions on conjugation are introduced. Necessary and sufficient stability conditions in these norms for weighted difference schemes are established. Convergence rate es...

After stating an abstract convergence result for the parareal algorithm used in the parallelization in time of general partial differential equations, we analyze the stability and convergence properties of the algorithm for equations with constant coefficients. We show that suitably damping coarse schemes ensure unconditional stability of the parareal algorithm and analyze how the regularity of...