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Showing papers in "Applied Numerical Mathematics in 2019"


Journal ArticleDOI
TL;DR: Five new explicit first-stage, singly diagonally-implicit Runge–Kutta (ESDIRK) methods are presented based on lessons learned from the review, including the only one of its kind sixth-order, L-stable, stage-order two, 6(5)-pair, ESDIRK included herein.

78 citations


Journal ArticleDOI
TL;DR: In this paper, the existence, uniqueness, and structural stability of solutions to nonlinear tempered fractional differential equations involving the Caputo tempered fractions derivative with generalized boundary conditions were studied and a singularity preserving spectral-collocation method for numerical solution of such equations was developed.

62 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of relevant non-dimensional governing physical parameters on velocity, energy and concentration profiles along with wall friction factor, wall heat and mass transfer coefficients are deliberated with help of graphs and tables.

58 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new numerical algorithm for solving the MHD equation by using the interpolating element free Galerkin (EFG) method to discrete the spatial direction.

56 citations


Journal ArticleDOI
TL;DR: Li and Wang as mentioned in this paper studied the existence, uniqueness, and regularity of the solutions of typical Caputo-type partial differential equations via the local discontinuous Galerkin (LDG) finite element methods.

54 citations


Journal ArticleDOI
TL;DR: Two new implicit–explicit, additive Runge–Kutta ( ARK 2 ) methods are given with fourth- and fifth-order formal accuracies, respectively, which are likely best suited to mildly stiff problems with tight error tolerances.

45 citations


Journal ArticleDOI
TL;DR: The proposed discretization algorithm follows the Du Fort–Frankel method and the unconditional stability and the convergence of the scheme are analyzed.

39 citations


Journal ArticleDOI
TL;DR: In this article, a modified Hestenes-Stiefel (HS) spectral conjugate gradient (CG) method for monotone nonlinear equations with convex constraints is proposed based on projection technique.

38 citations


Journal ArticleDOI
TL;DR: In this paper, an optimal homotopy analysis approach is described to solve nonlinear fractional differential equations with fractional derivatives, where an auxiliary linear operator and corresponding optimal initial approximation are used to accelerate the convergence of series solutions.

36 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a split-step spectral Galerkin (SSSG) method for the Riesz space-fractional derivatives of the Schrodinger equation.

35 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed an interpolating stabilized EFG method for a neutral delay PDE with fractional derivative in terms of Caputo fractional derivatives, which is a generalized form of the other equations such that it contains a delay term.

Journal ArticleDOI
TL;DR: Numerical results show that the GRK algorithm with and without relaxation for ridge regression perform much better in iteration steps than the variants of RK and RGS algorithms, and the accelerated GRK algorithms with relaxation significantly outperforms all other algorithms in terms of both iteration counts and computing times.

Journal ArticleDOI
TL;DR: In this paper, a finite element approximation for a linear, first-order in time, unconditionally energy stable scheme proposed in [7] for solving the magneto-hydrodynamic equations was studied.

Journal ArticleDOI
TL;DR: In this article, a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time-fractional diffusion equation from the boundary measured data is studied, and a stability estimate of inverse coefficient problem is obtained based on the regularity of solution of direct problem and some generalized Gronwall inequalities.

Journal ArticleDOI
TL;DR: In this paper, a new family of fractional functions based on Chelyshkov wavelets for solving one-and two-variable distributed-order fractional differential equations was introduced, and the convergence of the fractional-order ChelyShkov wavelet bases is discussed.

Journal ArticleDOI
TL;DR: In this paper, a spectral collocation numerical scheme for the approximation of the solutions of stochastic fractional differential equations is presented, whose coefficient matrix can be computed by an automatic procedure, consisting of linear steps.

Journal ArticleDOI
TL;DR: A linearized finite element method (FEM) for solving the cubic nonlinear Schrodinger equation with wave operator is proposed and it is proved that the proposed method keeps the energy conservation in the given discrete norm.

Journal ArticleDOI
TL;DR: In this paper, a convergence analysis for the Grunwald-Letnikov discretisation of a Riemann-Liouville fractional initial value problem on a uniform mesh t m = m τ with m = 0, 1, …, M.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed the conservative linearized Galerkin finite element methods (FEMs) for the nonlinear Klein-Gordon-Schrodinger equation (KGSE) with homogeneous boundary conditions.

Journal ArticleDOI
TL;DR: In this paper, an alternating direction implicit (ADI) spectral method is developed based on Legendre spectral approximation in space and finite difference discretization in time for the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations.

Journal ArticleDOI
TL;DR: In this article, a computational scheme based on the Chebyshev cardinal wavelets for a new class of nonlinear variable-order (V-O) fractional quadratic integral equations (QIEs) is presented.

Journal ArticleDOI
TL;DR: In this article, a mixed virtual element method was proposed for a pseudostress-displacement formulation of the linear elasticity problem with nonhomogeneous Dirichlet boundary conditions.

Journal ArticleDOI
TL;DR: The symplectic scheme is presented for solving the space fractional Schrodinger equation with one dimension, and the space semi-discretization and the full discretization are shown to preserve some properties of the SFSE.

Journal ArticleDOI
TL;DR: In this article, the authors consider discretizations of the incompressible Navier-Stokes equations, written in the newly developed energy-momentum-angular momentum conserving (EMAC) formulation.

Journal ArticleDOI
TL;DR: Based on the fourth-order fractional-compact difference operator, a new difference scheme with convergence order O ( τ 2 + h 1 4 + h 2 4 ) is derived, where τ is the temporal stepsize, h 1 and h 2 are the spatial stepsizes, respectively as mentioned in this paper.

Journal ArticleDOI
TL;DR: In this paper, a unified way to construct smoothing functions for solving the absolute value equation associated with second-order cone (SOCAVE) was explored, and numerical comparisons were presented, which illustrate what kinds of smoothing function work well along with the smoothing Newton algorithm.

Journal ArticleDOI
TL;DR: In this article, the Fourier analysis of fully discrete bicompact fourth-order spatial approximation schemes for hyperbolic equations is carried out on the example of a model linear advection equation.

Journal ArticleDOI
TL;DR: A spectral Galerkin approximation of optimal control problem governed by Riesz fractional differential equation with control integral constraint is developed, where two-sided Jacobi polyfractonomials are used to approximate the state variable and variational discretization is used to discretize the control variable.

Journal ArticleDOI
TL;DR: In this paper, a numerical method to solve Volterra integral equations of the second kind arising in the single term fractional differential equations with initial conditions is proposed, which is based on the discrete Galerkin method.

Journal ArticleDOI
TL;DR: In this article, a transversal method of lines (TMoL) is proposed to semi-discretize the time derivative of the Richards' equation and then a system of second order differential equations in the space variable is derived.