Related papers: The computational complexity of the initial value …
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
A new Hamilton principle of convolutional type, completely compatible with the initial conditions of an IVP, has been proposed in a recent publication arXiv:1912.08490v1 [math-ph]. In the present paper the possible use of this principle for…
In this paper well-posedness is proved for an initial and boundary value problem (IBVP) relative to a large class of quasilinear hyperbolic systems, in $p+q$ equations, on a strip, arising from a model of $H_2O$-phase transitions in the…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small…
In a 1979 paper, K. Okamoto introduced the space of initial values for the six Painlev\'e equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase…
This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical…
We consider the first order autonomous differential equation (ODE) ${\bf x}'={\bf f}({\bf x})$ where ${\bf f}: {\mathbb R}^n\to{\mathbb R}^n$ is locally Lipschitz. For ${\bf x}_0\in{\mathbb R}^n$ and $h>0$, the initial value problem (IVP)…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
In this article, we introduce a fixed parameter tractable algorithm for computing the Turaev-Viro invariants TV(4,q), using the dimension of the first homology group of the manifold as parameter. This is, to our knowledge, the first…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
We present an efficient and parsimonious algorithm to solve mixed initial/final-value problems. The algorithm optimally limits the memory storage and the computational time requirements: with respect to a simple forward integration, the…
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
Quantum invariants in low dimensional topology offer a wide variety of valuable invariants of knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is…
In this paper we define a small variation of the Taylor method and a formula for the global error of this new numerical method that allows us to keep track of the round-off error and does not require previous knowledge of the exact…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…