相关论文: Exponential-sum-approximation technique for variab…
In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain $\Omega$. Firstly, a fully…
Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
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…
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…
The multi-term time-fractional mixed diffusion-wave equations (TFMDWEs) are considered and the numerical method with its error analysis is presented in this paper. First, a $L2$ approximation is proved with first order accuracy to the…
In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-\alpha)$, where $\alpha…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…
A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…
We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases…
We solve a fractional diffusion equation using a piecewise-constant, discontinuous Galerkin method in time combined with a continuous, piecewise-linear finite element method in space. If there are $N$ time levels and $M$ spatial degrees of…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise…