Related papers: The computational complexity of the initial value …
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…
We study the initial value problem associated to a higher dimensional version of the Benjamin-Ono equation. Our purpose is to establish local well-posedness results in weighted Sobolev spaces and to determinate according to them some sharp…
In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove…
The unified transform method (UTM) for analyzing initial-boundary value (IBV) problems provides an important generalization of the inverse scattering transform (IST) method for analyzing initial value problems. In comparison with the IST, a…
In this work, we study the initial-value problem associated with the Kuramoto-Sivashinsky equation. We show that the associated initial value problem is locally and globally well-posed in Sobolev spaces $H^s(\mathbb{R})$, where $s>1/2$. We…
Higher order boundary value problems (BVPs) play an important role modeling various scientific and engineering problems. In this article we develop an efficient numerical scheme for linear $m^{th}$ order BVPs. First we convert the higher…
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and…
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
We show that the initial value problem of a periodic box-ball system can be solved in an elementary way using simple combinatorial methods.
Errors in numerical simulations of gravitating systems can be magnified exponentially over short periods of time. Numerical shadowing provides a way of demonstrating that the dynamics represented by numerical simulations are representative…
Continuous-time models such as Neural ODEs and Neural Flows have shown promising results in analyzing irregularly sampled time series frequently encountered in electronic health records. Based on these models, time series are typically…
Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the…
Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…
We study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…
In this work, we investigate the IVP for a time-fractional fourth-order equation with nonlinear source terms. More specifically, we consider the time-fractional biharmonic with exponential nonlinearity and the time-fractional Cahn-Hilliard…
We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations by describing the boundary conditions of a spacetime metric in its associated gauge. This gauge is determined, equivariantly with respect to…
The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within…