Publication

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

2014
Student Projects

Abstract

In this report, we first introduce operator splitting as a way to solve nonlinear reaction-diffusion PDEs. We then present a flux-limiting technique for anisotropic diffusion problems that allows to recover the discrete maximum principle. Finally, we implement a simple action potential model, which allows us to represent the evolution of the transmembrane potential of a stimulated cell, and investigate the effect of anisotropic diffusion on the positivity of this potential.

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2014
Student Projects

Abstract

Official source

Related concepts (32)

Membrane potential

Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell. That is, there is a difference in the energy required for electric charges to move from the internal to exterior cellular environments and vice versa, as long as there is no acquisition of kinetic energy or the production of radiation. The concentration gradients of the charges directly determine this energy requirement.

Action potential

An action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells.

Resting potential

A relatively static membrane potential which is usually referred to as the ground value for trans-membrane voltage. The relatively static membrane potential of quiescent cells is called the resting membrane potential (or resting voltage), as opposed to the specific dynamic electrochemical phenomena called action potential and graded membrane potential. Apart from the latter two, which occur in excitable cells (neurons, muscles, and some secretory cells in glands), membrane voltage in the majority of non-excitable cells can also undergo changes in response to environmental or intracellular stimuli.

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Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

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