Showing papers in "Applied Numerical Mathematics in 2017"

TL;DR: In this paper, a high order numerical scheme for multi-dimensional variable-order fractional Schrdinger equations is proposed, which is based on the shifted Jacobi polynomials (SJPs).

TL;DR: In this article, a fractional evolution equation based on the Riemann-Liouville fractional integral is considered and a spectral element method is used to obtain a full-discrete scheme.

TL;DR: In this article, the authors discuss the efficient implementation of RKN-type Fourier collocation methods, which are used when solving second-order differential equations, and their proposed implementation relies on an alternative formulation of the methods and their blended formulation.

TL;DR: In this article, the numerical solution of the nonlinear fractional Ginzburg-Landau equation is studied, and the boundedness, existence and uniqueness of numerical solution are investigated in details.

TL;DR: This work investigates implicit-explicit (IMEX) Runge-Kutta (RK) methods for differential systems with non-stiff and stiff processes and describes the construction of IMEX RK methods, where the 'explicit part' of the schemes have strong stability properties.

TL;DR: In this article, a class of explicit balanced schemes for stochastic differential equations with coefficients of superlinearly growth satisfying a global monotone condition is introduced, and some numerical results are presented.

TL;DR: This paper focuses on theoretical and practical issues in using radial basis functions (RBF) for reconstructing implicit curves and surfaces from point clouds and study the conditioning of the problem.

TL;DR: A new numerical method is presented based on the approximation of the solution of the distributed order time-fractional diffusion equation by a double Chebyshev truncated series, and the subsequent collocation of the resulting discretised system of equations at suitable collocation points.

TL;DR: In this article, the authors present nonlinear stability and convergence analyses for a second order operator splitting scheme applied to the good Boussinesq equation, coupled with the Fourier pseudo-spectral approximation in space.

TL;DR: In this article, the authors provide a contribution to the model benchmarking and to the influence induced by the application of simplified models on the numerical simulations of flood events, overcoming some limitations that characterize part of the studies in the literature.

TL;DR: In this paper, a new set of functions called fractional-order Bernoulli functions (FBFs) were defined to obtain the numerical solution of linear and nonlinear fractional integro-differential equations.

TL;DR: In this article, a general class of diffusion problem is considered, where the standard time derivative is replaced by a fractional one, and a mixed method is proposed, which consists of a finite difference scheme through space and a spectral collocation method through time.

TL;DR: Numerical results show that the developed non-polynomial ENO and WENO methods with the monotone polynomial interpolation method enhance the local accuracy and give sharper solution profile than the ENO/WenO methods based on the polynometric interpolation.

TL;DR: In this article, the zeroth-order coefficient in a time-fractional diffusion equation from two boundary measurement data in one-dimensional case was identified by the Laplace transformation and Gel'fand-Levitan theory.

TL;DR: In this paper, the partially truncated Euler-Maruyama (EM) method is proposed for highly nonlinear stochastic differential equations (SDEs) and it is shown that the method can preserve the stability and boundedness of the underlying SDEs.

TL;DR: This paper considers the Monodomain model and resorts to Proper Orthogonal Decomposition techniques to take advantage of an off-line step when solving iteratively the electrocardiological forward model online, and performs the Discrete Empirical Interpolation Method (DEIM) to tackle the nonlinearity of the model.

TL;DR: This method has great potential to be useful for realistic problems involving coupled free flow and porous media flow and is convenient to implement, computationally efficient, mass conserving, optimally accurate, and able to handle complex geometries.

TL;DR: A mixed-type method, which unifies the best features of the accurate continuousdiscrete extended and cubature Kalman filters, and is examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn.

TL;DR: In this article, the inverse source problem for a time-fractional wave equation in a bounded domain in R d was studied and a numerical algorithm based on Rothe's method was proposed, a priori estimates were proved and convergence of iterates towards the solution was established.

TL;DR: In this paper, the authors proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile-immobile advection-dispersion model based on reproducing kernel theory and collocation method.

TL;DR: In this article, an adaptive moving least squares (MLS) method with variable radius of influence is presented to improve the accuracy of meshless local Petrov-Galerkin (MLPG) methods and to minimize the computational cost for the numerical solution of singularly perturbed boundary value problems.

TL;DR: In this paper, the convergence of a Dickson polynomial solution of the model problem is investigated by means of the residual function, and the exact solutions are compared with other well-known methods in tables.

TL;DR: The discontinuous Galerkin time stepping method for solving the linear space fractional partial differential equations with Riesz fractional derivative is considered.

TL;DR: In this article, the Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights.

TL;DR: In this article, the fractional cable equation can be changed into a system of integro-differential equations, and a full discrete numerical method for solving the system is studied, where in time axis the discontinuous Galerkin finite element method is used, and in spacial axis the GFE scheme is adopted.

TL;DR: In this paper, a class of functional differential equations with piecewise continuous arguments are solved using block boundary value methods (BBVMs) under the Lipschitz condition, and it is shown that the order of convergence of an extended BBVM coincides with its order of consistency.

TL;DR: In this paper, direct quadrature methods of arbitrary order for Volterra integral equations with periodic solution are presented, and the convergence of these methods is analyzed, and some numerical experiments are illustrated to confirm theoretical expectations and for comparison with other existing methods.

TL;DR: In this paper, a new Crank-Nicolson finite element method for the time-fractional subdiffusion equation is developed, in which a novel time discretization called the modified L1 method is used to discretize the Riemann-Liouville fractional derivative.

TL;DR: In this article, the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm 6 where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O ( Δ t 2 - α ), 0 < α < 1, where α is the order of fractional derivative and Δt is the step size.

TL;DR: In this paper, a modified Landweber iteration method via a gradient flow equation induced by a weighted least squares functional was proposed, which significantly reduces the number of iterations needed to match an appropriate stopping criterion.