An Improved Algorithm Based on Finite Difference Schemes for Fractional Boundary Value Problems with Nonsmooth Solution
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-017-0417-8
Abstract: In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with nonsmooth solution. Two popular finite difference schemes,… read more here.
Keywords: difference; nonsmooth solution; solution; fractional boundary ... See more keywords
Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives
Sign Up to like & getrecommendations! Published in 2018 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2017.1381336
Abstract: ABSTRACT We present second-order difference schemes for a class of parabolic problems with variable coefficients and mixed derivatives. The solvability, stability and convergence of the schemes are rigorously analysed by the discrete energy method. Using… read more here.
Keywords: coefficients mixed; difference; variable coefficients; mixed derivatives ... See more keywords
The Order of Convergence of Difference Schemes for Fractional Equations
Sign Up to like & getrecommendations! Published in 2017 at "Numerical Functional Analysis and Optimization"
DOI: 10.1080/01630563.2017.1297825
Abstract: ABSTRACT In this paper, we continue our research on convergence of difference schemes for fractional differential equations. Using implicit difference scheme and explicit difference scheme, we have a deal with the full discretization of the… read more here.
Keywords: schemes fractional; difference; order convergence; convergence difference ... See more keywords
Three semi-implicit compact finite difference schemes for the nonlinear partial integro-differential equation arising from viscoelasticity
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Modelling and Simulation"
DOI: 10.1080/02286203.2020.1720566
Abstract: ABSTRACT Three semi-implicit compact finite difference schemes are described for the nonlinear partial integro-differential equation arising from viscoelasticity. In our methods, the time derivative is approximated by the backward-Euler, Crank–Nicolson-type and formally second-order backward differentiation… read more here.
Keywords: difference; three semi; compact finite; finite difference ... See more keywords
Construction of invariant compact finite-difference schemes.
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DOI: 10.1103/physreve.101.023303
Abstract: In this paper we propose a method, which is based on equivariant moving frames, for development of high-order accurate invariant compact finite-difference schemes that preserve Lie symmetries of underlying partial differential equations. In this method,… read more here.
Keywords: invariant compact; difference schemes; symmetry; finite difference ... See more keywords
Compact Difference Schemes on a Three-Point Stencil for Second-Order Hyperbolic Equations
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DOI: 10.1134/s0012266121070090
Abstract: We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable coefficients. New compact schemes are proposed for one type of second-order quasilinear… read more here.
Keywords: difference; order; second order; three point ... See more keywords
Difference Schemes Based on the Laguerre Transform
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DOI: 10.1134/s0965542521030131
Abstract: Optimal difference schemes based on the Laguerre transform are proposed for solving the wave equation. Additional parameters are introduced into the difference scheme used for the equations of harmonics. Numerical values of these parameters are… read more here.
Keywords: laguerre transform; based laguerre; optimal difference; difference schemes ... See more keywords
Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation
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DOI: 10.1186/s13662-020-02584-2
Abstract: We consider the generalized KdV–Burgers KdVB ( p , m , q ) $\operatorname{KdVB}(p,m,q)$ equation. We have designed exact and consistent nonstandard finite difference schemes (NSFD) for the numerical solution of the KdVB ( 2… read more here.
Keywords: difference; equation; finite difference; nsfd scheme ... See more keywords
On the convergence of difference schemes for the generalized BBM–Burgers equation
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DOI: 10.1515/gmj-2018-0075
Abstract: Abstract A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each… read more here.
Keywords: difference; generalized bbm; burgers equation; convergence difference ... See more keywords
Construction of Compact Finite Difference Schemes by Classic Differential Quadrature
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DOI: 10.3390/app7030284
Abstract: Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods. The derived difference… read more here.
Keywords: classic differential; quadrature; differential quadrature; finite difference ... See more keywords
Approximate Solutions for a Class of Predator-Prey Systems with Nonstandard Finite Difference Schemes
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DOI: 10.3390/sym14081660
Abstract: In this paper, we construct new nonstandard finite difference schemes to approximate a set of positive solutions for the predator–prey model, which contains different functional responses. The organization of the denominator of the discrete derivative… read more here.
Keywords: nonstandard finite; predator prey; difference schemes; finite difference ... See more keywords