We construct an original framework based on convex analysis to prove the existence and uniqueness of a solution class implicit numerical schemes. propose application this general in case new non linear scheme for 1D Lagrangian gas dynamics equations. provide illustrations that corroborate our proof unconditional stability scheme.

Abstract We devise a numerical scheme for computing arc-length parameterized curves of low bending energy that are confined to convex domains. address the convergence discrete formulations continuous model and unconditional stability an iterative scheme. Numerical simulations confirm theoretical results lead classification observed optimal within spheres.

This paper presents a fast and simple method for solving the shallow water equations. The water velocity and height variables are collocated on a uniform grid and a novel, unified scheme is used to advect all quantities together. Furthermore, we treat the fluid as weakly compressible to avoid solving a pressure Poisson equation. We sacrifice accuracy and unconditional stability for speed, but w...

Split-step procedures have previously been used successfully in a number of situations, e.g. for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note that one particular way to write the 3-D Maxwell’s equations separates these into two parts, requiring in all only the solution of six uncoupled 1-D wave equations. The approach allows arbitrary orders of accuracy ...

The object of this investigation * was to determine the possibility of forming a conditioned knee jerk, and, if formed, to study the rate of its formation, its stability, and the effect of varying such factors in the procedure as length of training and the conditioning stimulus. Finally, it was desired to study the course of contraction in the conditioned and unconditional knee jerks and in the...

We propose and analyze the spectral collocation approximation for the partial integrodifferential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomia...

Abstract. We apply wavelets to study the generalized local Morrey-Campanato spaces Mφ,p(R) and their preduals. As applications, we characterize the multipliers on Mφ,p(R) and the stability of these spaces under the perturbation of Calderón-Zygmund operators. Our results indicate that there exist some Mφ,p(R) without unconditional basis. This fact shows that Mφ,p(R) have some different character...

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2). The presented numerical scheme is based on the L2-1σ method in time and the Galerkin finite element method in space. The unconditional stability and ...