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Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

We propose two localized Radial Basis Function (RBF) methods, the Radial Basis Function Partition of Unity method (RBF-PUM) and the Radial Basis Function generated Finite Differences method (RBF-FD), for solving financial derivative pricing…

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

Meshless methods approximate operators in a specific node as a weighted sum of values in its neighbours. Higher order approximations of derivatives provide more accurate solutions with better convergence characteristics, but they come at…

In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…

Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as…

Performing density functional theory (DFT) calculations requires a careful choice of computational parameters to ensure convergence and obtain meaningful results. This represents a particularly important problem for high-throughput and…

Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs)…

We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and…

We propose a new framework for efficiently sampling from complex probability distributions using a combination of normalizing flows and elliptical slice sampling (Murray et al., 2010). The central idea is to learn a diffeomorphism, through…

In this paper we introduce a new, simple and efficient numerical scheme for the implementation of the freezing method for capturing similarity solutions in partial differential equations. The scheme is based on an IMEX-Runge-Kutta approach…

Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…

The cubic spline interpolation method, the Runge--Kutta method, and the Newton-Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated…

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…

An efficient algorithm without flux correction for simulation of corona discharges is proposed. The algorithm referred to as the position-state separation method (POSS) is used to solve convection-dominated continuity equations commonly…

We have developed a parallel algorithm for radial basis function (RBF) interpolation that exhibits O(N) complexity,requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a GMRES iterative solver with a…