Related papers: Discussion on exp-function method and modified met…
We provide new exact Taylor's series with fixed coefficients and without the remainder. We demonstrate the usefulness of this contribution by using it to obtain very simple solutions to (non-linear) PDEs. We also apply the method to the…
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schr\"odinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic…
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the…
Properties of the wave function equivalent potentials introduced by HAL QCD collaboration are studied in a non-relativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and…
We study damped wave propagation problems phrased as abstract evolution equations in Hilbert spaces. Under some general assumptions, including a natural compatibility condition for initial values, we establish exponential decay estimates…
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity…
In this paper we study nonlinear partial differential equations (PDEs) that are used to model different value adjustments denoted generally as xVA. These adjustments are nowadays commonly added to the risk-free financial derivative values…
Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study…
The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be…
In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.
This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE)…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and…
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…