The objective of this paper is to obtain an approximate solution for some well-known linear and nonlinear two-point boundary value problems. For this purpose, a semianalytical method known as optimal homotopy asymptotic method (OHAM) is used. Moreover, optimal homotopy asymptotic method does not involve any discretization, linearization, or small perturbations and that is why it reduces the computations a lot. OHAM results show the effectiveness and reliability of OHAM for application to two-point boundary value problems. The obtained results are compared to the exact solutions and homotopy perturbation method (HPM).

This paper studies continuous nonlinear economic dynamics with a continuous delay of a Kaldor type modified in dimension two. The important results are, on the one hand, the boundedness of solutions, the existence of an attractive set, and the permanence of the system and, on the other hand, the local and global stability of equilibrium points.

This paper is concerned with the analysis of the linear $\theta$-method and compact $\theta$-method for solving delay reaction-diffusion equation. Solvability, consistence, stability, and convergence of the two methods are studied. When $\theta \in [\mathrm{0},\mathrm{1}/\mathrm{2})$, sufficient and necessary conditions are given to show that the two methods are asymptotically stable. When $\theta \in [\mathrm{1}/\mathrm{2},\mathrm{1}]$, the two methods are proven to be unconditionally asymptotically stable. Finally, several examples are carried out to confirm the theoretical results.

This paper is concerned with stability analysis of additive Runge-Kutta methods for delay-integro-differential equations. We show that if the additive Runge-Kutta methods are algebraically stable, the perturbations of the numerical solutions are controlled by the initial perturbations from the system and the methods.

We consider the following nonlinear parabolic equation: $u_t-\mathrm{d}\mathrm{i}\mathrm{v}(|\nabla u{|}^{p(x)-\mathrm{2}}\nabla u)=f(x,t)$, where $f:\mathrm{\Omega }\times (\mathrm{0},T)\to \mathbb{R}$ and the exponent of nonlinearity $p(·)$ are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions.