Correction to: Explicit Third-Order Unconditionally Structure-Preserving Schemes for Conservative Allen–Cahn Equations

Unconditionally Stable Schemes for Higher Order Inpainting

Abstract. Inpainting methods with third and fourth order equations have certain advantages in comparison with equations of second order such as the smooth interpolation of image information even over large distances. Because of this such methods became very popular in the last couple of years. Solving higher order equations numerically can be a computational demanding task though. Discretizing ...

Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

Simulation of Proposed On-Line Third Order Resonance Correction Schemes

Conservative semi-Lagrangian schemes for Vlasov equations

Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case...

Unconditionally Stable Schemes for Equations of Thin Film Epitaxy

dx. The construction of the schemes involves an appropriate extension of Eyre’s idea of convex-concave decomposition of the energy functional. As an application, we derive unconditionally stable and convergent schemes for epitaxial film growth models with slope selection (F (y) = 1 4 (|y| − 1)) and without slope selection (F (y) = − 1 2 ln(1 + |y|)). We conclude the paper with some preliminary ...