Related papers: On a collocation method for the time-fractional co…
This paper presents a novel semi-analytical collocation method to solve multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method it employs the Fourier series expansion for spatial…
A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the…
In this paper, we present a robust and fully discretized method for solving the time fractional diffusion equation with high-contrast multiscale coefficients. We establish the homogenized equation using a multicontinuum approach and employ…
The purpose of this paper is to propose a new algorithm for obtaining approximate solutions to the Burgers' equation (BE). Integration in time by a quadratic B-spline collocation method is shown. To the best of our knowledge, B-splines have…
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…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for…
This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…
This paper presents a linear computational technique based on cubic trigonometric cubic B-splines for time fractional burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient…
We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…
In this work, we present a collocation method based on the Legendre wavelet combined with the Gauss--Jacobi quadrature formula for solving a class of fractional delay-type integro-differential equations. The problem is considered with…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
In this paper, we develop a second-order accurate time-stepping scheme for the tempered time-fractional advection-dispersion equation based on a sum-of-exponentials (SOE) approximation to the convolution kernel involved in the fractional…