Recently developed kinetic theory for neuronal network dynamics has been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The kinetic equations are a system of (1+1)dimensional nonlinear partial differential equations (PDE) on a bounded domain with the following features: (i) the boundary conditions are nonlinear and...

A functionally graded material beam with generalized boundary conditions is contemplated in the present study in order to examine the deformation and stress behavior under thermal and thermo-mechanical load. Three discrete combinations of functionally graded materials have been deliberate in including a wide range of materials and material properties. The variation of material properties has be...

Optimal boundary closures are derived for first derivative, finite difference operators of order 2, 4, 6 and 8. The closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids and entropy stability for nonlinear equations that support a convex extension. The new closures are developed by enriching con...

Brief description of a FORTRAN 77 program for calculating energy values, refection and transmission matrices, and corresponding wave functions in a coupled-channel approximation of the adiabatic approach is presented. In this approach, a multidimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with the homogene...

We consider an algorithm called FEMWARP for warping tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a twoor three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its int...

An investigation has been carried out to obtain the flow and heat transfer of two dimensional electrically conducting second grade fluids over stretching surface in the presence of uniform magnetic field. The viscosity is assumed to vary as inverse linear function of temperature. The non-linear boundary layer equations together with the boundary conditions are reduced to a system of non-linear ...

In this article, a shifted Legendre tau method is introduced to get a direct solution technique for solving multi-order fractional differential equations (FDEs) with constant coefficients subject to multi-point boundary conditions. The fractional derivative is described in the Caputo sense. Also, this article reports a systematic quadrature tau method for numerically solving multi-point boundar...

A new method will be introduced for the derivation of thermodynamically consistent boundary conditions for the full Cahn-Hilliard-Navier-Stokes-Fourier system for two immiscible fluids, where the phase field variable (order parameter) is given in terms of concentrations or partial densities. Five different types of models will be presented and discussed. The article can be considered as a conti...

Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

1 J. Hadamard's ideas of correct formulation of problems of mathematical physics as well as related Banach's theorem on the inverse operator are analyzed. Modern techniques of numerical simulations are shown to be in drastic contradiction to the concepts of J. Hadamard, S. Banach and a number of other outstanding scientists in the sense that the priority is given to the realization of inefficie...