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Abstract: Recently, numerical solutions of stochastic differential equations have received a great deal of attention. Numerical approximation schemes are invaluable tools for exploring their properties. In this paper, we introduce a class of stochastic age-dependent (vintage) capital system with Poisson jumps. We also give the discrete approximate solution with an implicit Euler scheme in time discretization. Using Gronwall’s lemma and Barkholder–Davis–Gundy’s inequality, some criteria are obtained for the exponential stability of numerical solutions to the stochastic age-dependent capital system with Poisson jumps. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions, where information on the order of approximation is provided. These error bounds imply strong convergence as the timestep tends to zero. A numerical example is used to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, it is considered for a class of stochastic age-structured population equations with diffusions and Markovian switching. Most kind of equations are nonlinear and cannot be solved explicitly, so the construction of efficient computational methods is of great importance. The main aim of this paper is to develop a numerical scheme and investigate the convergence of numerical approximation. An example is given for illustration. [Copyright &y& Elsevier]

The mechanical deformation of an ideal thin-walled cylindrical shell is investigated in the presence of intersurface interactions with a planar rigid substrate. A Dugdale- Barenblatt-Maugis (DBM) cohesive zone approximation is introduced to simulate the convoluted surface force potential. Without loss of generality, the repulsive component of the surface forces is approximated by a linear soft-repulsion, and the attractive component is described by two essential variables, namely, surface force range and magnitude, which are allowed to vary. The nonlinear problem is solved numerically to generate the pressure distribution within the contact, the deformed membrane profiles, and the adhesion-delamination mechanics, which are distinctly different from the classical solid cylinder adhesion models. The model has wide applications in cell adhesion and nanostructures. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a class of stochastic age-dependent population equations with Markovian switching is considered. The main aim of this paper is to investigate the convergence of the numerical approximation of stochastic age-dependent population equations with Markovian switching. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. An example is given for illustration. [Copyright &y& Elsevier]

Abstract: In this paper, a class of stochastic pantograph equations with Markovian switching is considered. The main purpose is to investigate the convergence of the Euler method of the equations. It is proved that the Euler approximation solution converge to the analytic solution in probability under weaker conditions. An example is provided to illustrate our theory. [Copyright &y& Elsevier]