Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2017, Volume 316, pp. 109 - 121

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initialâ€“boundary value problems of...

Mixed derivatives | High-order ADI scheme | Option pricing | Stochastic volatility models | MATHEMATICS, APPLIED | FINITE-DIFFERENCE SCHEMES | STABILITY | EQUATIONS | CONVERGENCE | COMPACT SCHEMES | Analysis | Models | Pricing | Alternating direction implicit methods | Volatility | Mathematical analysis | Mathematical models | Derivatives | Stochasticity | Finite difference method

Mixed derivatives | High-order ADI scheme | Option pricing | Stochastic volatility models | MATHEMATICS, APPLIED | FINITE-DIFFERENCE SCHEMES | STABILITY | EQUATIONS | CONVERGENCE | COMPACT SCHEMES | Analysis | Models | Pricing | Alternating direction implicit methods | Volatility | Mathematical analysis | Mathematical models | Derivatives | Stochasticity | Finite difference method

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

The sub-grid-scale parameterization of clouds is one of the weakest aspects of weather and climate modeling today, and the explicit simulation of clouds will...

76R10 | Numerical weather prediction | 65M06 | Numerical methods | 76U05 | 76E06 | 86A10 | 65M12 | Time splitting | Compressible flow | SYSTEM | numerical methods | time splitting | compressible flow | CONVECTION | EQUATIONS | MESOSCALE MODEL | SIMULATION | FORMULATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | numerical weather prediction | DYNAMICS | ADVECTION | TURBULENCE | SCHEMES | Usage | Weather forecasting | Models

76R10 | Numerical weather prediction | 65M06 | Numerical methods | 76U05 | 76E06 | 86A10 | 65M12 | Time splitting | Compressible flow | SYSTEM | numerical methods | time splitting | compressible flow | CONVECTION | EQUATIONS | MESOSCALE MODEL | SIMULATION | FORMULATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | numerical weather prediction | DYNAMICS | ADVECTION | TURBULENCE | SCHEMES | Usage | Weather forecasting | Models

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

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 | Î¸-schemes

35B35 | 65M06 | analytical stability | piecewise constant arguments | numerical stability | 65M12 | Partial differential equation | Î¸-schemes

Journal Article

Bulletin of Mathematical Biology, ISSN 0092-8240, 12/2018, Volume 80, Issue 12, pp. 3184 - 3226

We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures...

Life Sciences, general | 92C37 | Mathematical and Computational Biology | Poroelasticity | 65M06 | Interstitial fluid pressure | Mathematics | Mathematical biology | ECM degradation | Drug distribution in tissue | 65M12 | Cell Biology | INTERSTITIAL PRESSURE | DRUG-RESISTANCE | SKELETAL-MUSCLE | MATHEMATICAL-MODEL | DEFORMABLE POROUS-MEDIA | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EXTRACELLULAR-MATRIX | FLUID TRANSPORT | GENE-TRANSFER | MONOCLONAL-ANTIBODIES | TRANSCAPILLARY PRESSURE-GRADIENT | Neoplasms - metabolism | Enzyme Therapy | Extracellular Matrix - drug effects | Humans | Elasticity | Extracellular Matrix - metabolism | Mathematical Concepts | Linear Models | Pressure | Neoplasms - drug therapy | Biomechanical Phenomena | Extracellular Fluid - metabolism | Algorithms | Animals | Models, Biological | Computer Simulation | Porosity | Nonlinear Dynamics | Antimitotic agents | Enzymes | Chemotherapy | Numerical analysis | Analysis | Models | Antineoplastic agents | Health aspects | Cancer | Computer simulation | Cancer therapies | Matrix methods | Fluid pressure | Mechanical analysis | Degradation | Mathematical analysis | Continuum mechanics | Mathematical models | Pretreatment | Transport | Tumors | Analysis of PDEs

Life Sciences, general | 92C37 | Mathematical and Computational Biology | Poroelasticity | 65M06 | Interstitial fluid pressure | Mathematics | Mathematical biology | ECM degradation | Drug distribution in tissue | 65M12 | Cell Biology | INTERSTITIAL PRESSURE | DRUG-RESISTANCE | SKELETAL-MUSCLE | MATHEMATICAL-MODEL | DEFORMABLE POROUS-MEDIA | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EXTRACELLULAR-MATRIX | FLUID TRANSPORT | GENE-TRANSFER | MONOCLONAL-ANTIBODIES | TRANSCAPILLARY PRESSURE-GRADIENT | Neoplasms - metabolism | Enzyme Therapy | Extracellular Matrix - drug effects | Humans | Elasticity | Extracellular Matrix - metabolism | Mathematical Concepts | Linear Models | Pressure | Neoplasms - drug therapy | Biomechanical Phenomena | Extracellular Fluid - metabolism | Algorithms | Animals | Models, Biological | Computer Simulation | Porosity | Nonlinear Dynamics | Antimitotic agents | Enzymes | Chemotherapy | Numerical analysis | Analysis | Models | Antineoplastic agents | Health aspects | Cancer | Computer simulation | Cancer therapies | Matrix methods | Fluid pressure | Mechanical analysis | Degradation | Mathematical analysis | Continuum mechanics | Mathematical models | Pretreatment | Transport | Tumors | Analysis of PDEs

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

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 Â âˆ’Â u xxt Â +Â 3uu x Â âˆ’Â 2u x u xx Â âˆ’Â uu xxx Â =Â 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

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

9.
Full Text
Free boundary problem for cell protrusion formations: theoretical and numerical aspects

Journal of Mathematical Biology, ISSN 0303-6812, 8/2017, Volume 75, Issue 2, pp. 263 - 307

In this paper, a free boundary problem for cell protrusion formation is studied theoretically and numerically. The cell membrane is precisely described thanks...

Cell protrusion formation | 92C37 | Mathematical and Computational Biology | 65M06 | Mathematics | Mathematical biology | Applications of Mathematics | Free boundary problem | Finite differences on cartesian grids | 65M12 | MIGRATION | FLUID | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | INTERFACES | EQUATIONS | FLOWS | KERATOCYTES | Cell Membrane - chemistry | Signal Transduction | Models, Biological | Environment | Pseudopodia - physiology | Cell Membrane - physiology | Cell Movement | Chemical reactions | Cell membranes | Cell development (Biology) | Analysis | Leukocyte migration | Polymerization | Two dimensional models | Laplace equation | Pseudopodia | Well posed problems | Cell adhesion & migration | Signal transduction | Signaling | Actin | Chemical interactions | Dirichlet problem | Mathematical models | Cell migration | Elongation | Finite difference method | Analysis of PDEs

Cell protrusion formation | 92C37 | Mathematical and Computational Biology | 65M06 | Mathematics | Mathematical biology | Applications of Mathematics | Free boundary problem | Finite differences on cartesian grids | 65M12 | MIGRATION | FLUID | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | INTERFACES | EQUATIONS | FLOWS | KERATOCYTES | Cell Membrane - chemistry | Signal Transduction | Models, Biological | Environment | Pseudopodia - physiology | Cell Membrane - physiology | Cell Movement | Chemical reactions | Cell membranes | Cell development (Biology) | Analysis | Leukocyte migration | Polymerization | Two dimensional models | Laplace equation | Pseudopodia | Well posed problems | Cell adhesion & migration | Signal transduction | Signaling | Actin | Chemical interactions | Dirichlet problem | Mathematical models | Cell migration | Elongation | Finite difference method | Analysis of PDEs

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

B-spline quasi-interpolation | shock capturing method | 35D40 | Constantin Bacuta | Artificial viscosity | 65M06 | Conservation laws | Viscosity | Interpolation | Stability analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 7, pp. 2391 - 2425

We present a high-order cell-centered Lagrangian scheme for solving the two-dimensional gas dynamics equations on unstructured meshes. A node-based...

High-order finite volume methods | Unstructured mesh | Cell-centered scheme | Compressible flow | Lagrangian hydrodynamics | Generalized Riemann problem | INSTABILITY | ERRORS | SHOCK HYDRODYNAMICS | COMPUTATIONS | PHYSICS, MATHEMATICAL | ARTIFICIAL VISCOSITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | DYNAMICS | SYSTEMS | Fluid dynamics | Approximation | Computation | Mathematical analysis | Conservation | Entropy | Fluxes | Two dimensional | Compressible fluids | Mechanics | Mechanics of the fluids | Fluids mechanics | Engineering Sciences | Physics

High-order finite volume methods | Unstructured mesh | Cell-centered scheme | Compressible flow | Lagrangian hydrodynamics | Generalized Riemann problem | INSTABILITY | ERRORS | SHOCK HYDRODYNAMICS | COMPUTATIONS | PHYSICS, MATHEMATICAL | ARTIFICIAL VISCOSITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | DYNAMICS | SYSTEMS | Fluid dynamics | Approximation | Computation | Mathematical analysis | Conservation | Entropy | Fluxes | Two dimensional | Compressible fluids | Mechanics | Mechanics of the fluids | Fluids mechanics | Engineering Sciences | Physics

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

35R11 | variable order fractional cable equation | Crank-Nicolson method | stability analysis | 65M06 | 26A33 | MATHEMATICS

Journal Article

13.
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On the stability of Micken's type NSFD schemes for generalized Burgers Fisher equation

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

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

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 | Convectionâ€“diffusion equations | 65N12 | 65M06 | 65N06 | 76R05 | 65Y05 | MATHEMATICS, APPLIED | GRIDS | PARABOLIC EQUATIONS | ALGORITHM | Convection-diffusion equations | 2ND-ORDER ACCURACY | DECOMPOSITION | NUMERICAL-SOLUTION

Mass-preserving | Multi-block | Unconditional stability | S-DDM | Modified-upwind | Convectionâ€“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 Hamiltonâ€“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

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

17.
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A truly two-dimensional discretization of drift-diffusion equations on cartesian grids

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

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

A new method is proposed for estimating the rate of fugitive emissions of particulate matter from multiple time-dependent sources via measurements of...

Gaussian plume | Pollutant dispersion | Particle deposition | Bayesian estimation | Inverse problem | PERSPECTIVE | POLLUTANTS | RECONSTRUCTION | DEPOSITION | AIR | DIFFUSION EQUATION | FORMULATION | INVERSION | INFERENCE | ENVIRONMENTAL SCIENCES | ATMOSPHERIC DISPERSION | METEOROLOGY & ATMOSPHERIC SCIENCES | Case studies | Environmental aspects | Air pollution | Models | Emissions (Pollution) | Analysis | Statistics - Applications

Gaussian plume | Pollutant dispersion | Particle deposition | Bayesian estimation | Inverse problem | PERSPECTIVE | POLLUTANTS | RECONSTRUCTION | DEPOSITION | AIR | DIFFUSION EQUATION | FORMULATION | INVERSION | INFERENCE | ENVIRONMENTAL SCIENCES | ATMOSPHERIC DISPERSION | METEOROLOGY & ATMOSPHERIC SCIENCES | Case studies | Environmental aspects | Air pollution | Models | Emissions (Pollution) | Analysis | Statistics - Applications

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

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

Mathematics Subject Classification : 65M06 | PHASE-SEPARATION | MATHEMATICS, APPLIED | ELEMENT METHOD

Journal Article