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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2017, Volume 316, pp. 109 - 121
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 08/2017, Volume 56, Issue 4
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2008, Volume 227, Issue 7, pp. 3465 - 3485
Journal Article
SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics, ISSN 1064-8275, 2019, Volume 41, Issue 2, pp. A1170 - A1200
We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh... 
forced curve shortening flow | moving mesh methods | 53C44 | 65M06 | monitor functions | geometric partial differential equations | 65M50 | tangential redistribution | 53C80 | 35K65
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 12/2019, Volume 96, Issue 12, pp. 2352 - 2370
This paper deals with the analytical and numerical stability of a partial differential equation with piecewise constant arguments of alternately retarded and... 
35B35 | 65M06 | analytical stability | piecewise constant arguments | numerical stability | 65M12 | Partial differential equation | θ-schemes
Journal Article
Bulletin of Mathematical Biology, ISSN 0092-8240, 12/2018, Volume 80, Issue 12, pp. 3184 - 3226
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 02/2017, Volume 94, Issue 2, pp. 386 - 404
In this article, two characteristic block-centred finite difference schemes are introduced and analysed to solve the nonlinear convection-dominated diffusion... 
Characteristic block-centred finite difference | 65M15 | 65M25 | convection-dominated diffusion equation | two-grid | 65M06 | nonlinear | 65M55 | error estimates | 65M12 | MATHEMATICS, APPLIED | ELEMENT-METHOD | ELLIPTIC PROBLEMS | Diffusion | Nonlinear equations | Errors | Diffusion barriers | Mathematical analysis | Images | Nonlinearity | Mathematical models | Finite difference method
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 10/2007, Volume 32, Issue 10, pp. 1511 - 1549
We show that the Camassa-Holm equation u t  − u xxt  + 3uu x  − 2u x u xx  − uu xxx  = 0 possesses a global continuous semigroup of weak conservative solutions... 
Secondary 35B10, 35Q53 | Primary 65M06, 65M12 | Conservative solutions | Camassa-Holm equation | MATHEMATICS | BREAKING | SCHEME | MATHEMATICS, APPLIED | GEOMETRIC APPROACH | WAVES | conservative solutions | ROD | WEAK SOLUTIONS | camassa-holm equation | SHALLOW-WATER EQUATION | PEAKONS
Journal Article
Applicable Analysis, ISSN 0003-6811, 01/2020, Volume 99, Issue 1, pp. 158 - 179
In general, B-spline quasi-interpolation (BSQI)-based numerical schemes for hyperbolic conservation laws are unstable in nature. In the present work, we have... 
B-spline quasi-interpolation | shock capturing method | 35D40 | Constantin Bacuta | Artificial viscosity | 65M06 | Conservation laws | Viscosity | Interpolation | Stability analysis
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 03/2018, Volume 38, Issue 2, pp. 580 - 590
In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described... 
35R11 | variable order fractional cable equation | Crank-Nicolson method | stability analysis | 65M06 | 26A33 | MATHEMATICS
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 12/2019, Volume 25, Issue 12, pp. 1706 - 1737
We propose exact finite difference scheme (EFD) for Generalized Burgers Fisher (GBF) Equation using solitary wave solution. Moreover a non-standard finite... 
Non-standard finite difference scheme | 35K61 | exact finite difference scheme | generalized Burgers Fisher | positivity | 65M06 | nonlinear | boundedness | Formulas (mathematics) | Solitary waves | Finite difference method
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 09/2019, Volume 96, Issue 9, pp. 1861 - 1878
We propose second-order linearly implicit predictor-corrector schemes for diffusion and reaction-diffusion equations of distributed-order. For diffusion... 
Predictor-corrector methods | matrix transfer technique | non-smooth initial data | distributed-order space-fractional differential equations | nonlinear PDEs | fractional Laplacian | 65M06 | 35R11 | 65M12 | MATHEMATICS, APPLIED | DIFFUSION
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2017, Volume 317, pp. 247 - 273
In the paper, a new mass-preserving and modified-upwind S-DDM scheme over non-overlapping multi-block sub-domains for solving time-dependent... 
Mass-preserving | Multi-block | Unconditional stability | S-DDM | Modified-upwind | Convection–diffusion equations | 65N12 | 65M06 | 65N06 | 76R05 | 65Y05 | MATHEMATICS, APPLIED | GRIDS | PARABOLIC EQUATIONS | ALGORITHM | Convection-diffusion equations | 2ND-ORDER ACCURACY | DECOMPOSITION | NUMERICAL-SOLUTION
Journal Article
Numerische Mathematik, ISSN 0029-599X, 7/2019, Volume 142, Issue 3, pp. 525 - 575
This paper is concerned with monotone (time-explicit) finite difference scheme associated with first order Hamilton–Jacobi equations posed on a junction. It... 
Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 65M12 | 49L25 | MATHEMATICS, APPLIED
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 5, pp. 2845 - 2870
genuinely two-dimensional discretization of general drift-diffusion (including incompressible Navier-Stokes) equations is proposed. Its numerical fluxes are... 
Bubbles | Drift-diffusion | Green-Dirichlet function | Navier-Stokes-Coriolis | drift-diffusion | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | SINGULAR PERTURBATION PROBLEM | FINITE-ELEMENT METHODS | ADVECTION | bubbles | MODEL | SCHEMES | Mathematics
Journal Article
Atmospheric Environment, ISSN 1352-2310, 09/2016, Volume 141, pp. 122 - 138
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1753 - 1776
In this paper, we devise an efficient dissipation-preserving fourth-order difference solver for the fractional-in-space nonlinear wave equations. First of all,... 
Computational Mathematics and Numerical Analysis | Stability | Dissipation-preserving scheme | Theoretical, Mathematical and Computational Physics | 65M06 | Mathematics | Convergence | Algorithms | Mathematical and Computational Engineering | 35R11 | Solvability | 65M12 | Finite difference methods | MATHEMATICS, APPLIED
Journal Article
Numerische Mathematik, ISSN 0029-599X, 02/2001, Volume 87, Issue 4, pp. 675 - 699
We propose a stable and conservative finite difference scheme to solve numerically the Cahn-Hilliard equation which describes a phase separation phenomenon.... 
Mathematics Subject Classification : 65M06 | PHASE-SEPARATION | MATHEMATICS, APPLIED | ELEMENT METHOD
Journal Article