Related papers: On Numerical Algorithms for the Solution of a Belt…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…
For the non cutoff radially symmetric homogeneous Boltzmann equation with Maxwellian molecules, we give the numerical solutions using symbolic manipulations and spectral decomposition of Hermit functions. The initial data can belong to some…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…
We consider the numerical solution of the equation - \Delta u - f(u) = g, for the unknown u satisfying Dirichlet conditions in a bounded domain. The nonlinearity f has bounded, continuous derivative. The algorithm uses the finite element…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
A fast numerical algorithm for the evolution of parton distributions in x space is described. The method is close in spirit to `brute' force techniques. The necessary integrals are performed by summing the approximate contributions from…
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of…
The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of the numerical solutions of FDEs whose solutions are…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…