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Journal of Differential Equations, ISSN 0022-0396, 04/2016, Volume 260, Issue 7, pp. 5847 - 5874
This paper proves the global existence and boundedness of solutions to a general reaction–diffusion predator–prey system with prey-taxis defined on a smooth... 
Global existence | Reaction–diffusion system with prey-taxis | Uniform persistence | Predator–prey model | Boundedness | Predator-prey model | Reaction-diffusion system with prey-taxis
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2019, Volume 50, pp. 448 - 468
This paper investigates a class of elliptic systems consisting of the p(x)-Laplacian equation and the Poisson equation for image denoising. Under the... 
[formula omitted] data | Elliptic system | Discontinuous variable exponent | Image denoising | Fixed points (mathematics) | Boundary value problems | Noise reduction | Images | Laplace equation | Poisson equation | Iterative methods
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 03/2017, Volume 332, p. 83
Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and... 
Approximation | Structural stability | Shooting | Approximations | Mathematical functions | Integrators | Spectra | Spectral methods | Energy conservation | Mechanics | Collocation methods | Galerkin method | Computational physics | Computational efficiency | Computing time | Hamiltonian functions | Calculus of variations | Energy conversion efficiency
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2012, Volume 50, Issue 5, pp. 2336 - 2356
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2016, Volume 85, Issue 299, pp. 1225 - 1261
are used. Our analysis is valid for arbitrary nonuniform regular meshes and for both periodic boundary conditions and for initial-boundary value problems. We... 
Conservation laws | Error estimates | Discontinuous galerkin method | Upwind-biased flux | SEMIDISCRETE | Discontinuous Galerkin method | FULLY DISCRETE | MATHEMATICS, APPLIED | SUPERCONVERGENCE | STABILITY | upwind-biased flux | RUNGE-KUTTA SCHEMES | conservation laws | SCALAR CONSERVATION-LAWS | SYSTEMS | WAVE-EQUATION | error estimates | FINITE-ELEMENT-METHOD | DG METHOD
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 06/2020, Volume 152, pp. 355 - 378
In this work, we study a new spectral Petrov-Galerkin approximation of space-time fractional reaction-diffusion equations with viscosity terms built by... 
Viscosity term | Spectral method | Error estimate | Fractional derivative
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2018, Volume 86, pp. 194 - 199
In this letter, a new reproducing kernel collocation method is presented for solving nonlocal fractional boundary value problems with non-smooth solutions. The... 
Reproducing kernel | Non-smooth solutions | Fractional order | Approximate solutions | MATHEMATICS, APPLIED | NUMERICAL-METHOD | ALGORITHM | HILBERT-SPACE | FUNCTIONAL-DIFFERENTIAL EQUATIONS
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 3/2019, Volume 78, Issue 3, pp. 1305 - 1328
Journal Article
Numerical Algorithms, ISSN 1017-1398, 12/2019, Volume 82, Issue 4, pp. 1221 - 1250
Journal Article
Computers & Mathematics with Applications, ISSN 0898-1221, 09/2018, Volume 76, Issue 5, p. 1056
Image denoising is a challenging task in the fields of image processing and computer vision. Inspired by the good performance of nonlinear fourth-order models... 
Computer vision | Diffusion rate | Partial differential equations | Image processing | Noise reduction | Existence theorems | Nonlinear differential equations | Entropy | Entropy of solution | Fixed points (mathematics) | Mathematical models | Diffusion | Vision systems | Curvature | Image processing systems
Journal Article
Plant Physiology, ISSN 0032-0889, 2/2017, Volume 173, Issue 2, pp. 1235 - 1246
Arabidopsis EXTRA-LARGE G PROTEINs interact with two PUB proteins in mediating the cytokinin response and multiple developmental processes. Heterotrimeric... 
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2017, Volume 311, pp. 387 - 393
Based on reproducing kernel theory, a numerical method is proposed for solving variable order fractional boundary value problems for functional differential... 
Reproducing kernel method | Boundary value problems | Fractional order | Variable order | NUMERICAL-METHODS | MATHEMATICS, APPLIED | ANOMALOUS SUBDIFFUSION EQUATION | SPATIAL ACCURACY | APPROXIMATION | DERIVATIVE MODEL | DISPERSION | DIFFUSION EQUATION | SPACE | DELAY | Methods | Differential equations | Kernels | Reproduction | Computation | Mathematical analysis | Mathematical models | Polynomials
Journal Article
International Journal of Numerical Methods for Heat & Fluid Flow, ISSN 0961-5539, 01/2014, Volume 24, Issue 6, pp. 1331 - 1337
Purpose - The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems.... 
Journal Article
International Journal of Numerical Methods for Heat & Fluid Flow, ISSN 0961-5539, 01/2014, Volume 24, Issue 7, pp. 1545 - 1552
Purpose - The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal... 
Heat sources | Approximation | Computational fluid dynamics | Mathematical analysis | Exact solutions | Mathematical models | Boundaries | Iterative methods
Journal Article
International Journal of Numerical Methods for Heat & Fluid Flow, ISSN 0961-5539, 01/2014, Volume 24, Issue 6, pp. 1331 - 1337
Purpose - The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems.... 
Heat sources | Inverse problems | Deformation | Perturbation methods | Mathematical analysis | Exact solutions | Mathematical models | Inverse
Journal Article
International Journal of Numerical Methods for Heat & Fluid Flow, ISSN 0961-5539, 01/2014, Volume 24, Issue 7, pp. 1545 - 1552
Purpose - The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal... 
Heat sources | Approximation | Computational fluid dynamics | Mathematical analysis | Exact solutions | Mathematical models | Boundaries | Iterative methods
Journal Article
International Journal of Numerical Methods for Heat & Fluid Flow, ISSN 0961-5539, 01/2014, Volume 24, Issue 7, pp. 1545 - 1552
Purpose - The purpose of this paper is to investigate the inverse problem of determining a time-dependent heat source in a parabolic equation with nonlocal... 
Journal Article
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