Geometrically nonlinear analysis of thin circular plates on Winkler elastic foundations has been studied in this paper. The nonlinear partial differential equations obtained from von Karman’s large deflection plate theory have been solved by using the discrete singular convolution (DSC) in the space domain and the harmonic differential quadrature (HDQ) method in the time domain.

A vectorial nonlocal linear hyperbolic problem with applications in superconductors of type-I is studied. The nonlocal term is represented by a (space) convolution with a singular kernel, which is arising in Eringen’s model. The well-posedness of the problem is discussed under low regularity assumptions and the error estimates for two time-discrete schemes (based on backward Euler approximation...

We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric singular perturbation theory in several examples. We also present numerical evidence for the dependence of unpinning asymptotics on regularity of the nonlocal convo...

This communication introduces a novel scheme for the treatment of free edge supports in the analysis of beams by using the discrete singular convolution (DSC) algorithm. Accommodating free edges has been a challenging issue in the DSC analysis of beams, plates, and shells. An iteratively matched boundary (IMB) method is proposed to overcome the difficulty. Numerical experiments are carried out ...

*Correspondence: [email protected] School of Mathematical Science, Qufu Normal University, Jingxuanxi Road 57, Qufu, Shandong 273165, P.R. China Abstract One class of singular integral equations of convolution type with Hilbert kernel is studied in the space L2[–π ,π ] in the article. Such equations can be changed into either a system of discrete equations or a discrete jump problem depending o...