Displaying similar documents to “An efficient approach for solving a class of nonlinear 2 D parabolic PDEs.”

Modeling and computation of heterogeneous implicit solvent and its applications for biomolecules

Duan Chen (2014)

Molecular Based Mathematical Biology


Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the form of total free energy functional and a quasi-linear Poisson-Boltzmann equation (QPBE)...

Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications

Jürgen Geiser (2009)

ESAIM: Mathematical Modelling and Numerical Analysis


Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We...

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

Roland Ernst, Bernd Flemisch, Barbara Wohlmuth (2009)

ESAIM: Mathematical Modelling and Numerical Analysis


A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.

A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations

Abigail Wacher (2013)

Open Mathematics


We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium...