Document Type

Article

Publication Date

3-15-2018

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We solve the first order 2-D reaction–diffusion equations which describe binding-diffusion kinetics using the photobleaching scanning profile of a confocal laser scanning microscope, approximated by a Gaussian laser profile. We show how to solve the first-order photobleaching kinetics partial differential equations (PDEs) using a time-stepping method known as a Krylov subspace spectral (KSS) method. KSS methods are explicit methods for solving time-dependent variable-coefficient partial differential equations. They approximate Fourier coefficients of the solution using Gaussian quadrature rules in the spectral domain. In this paper, we show how a KSS method can be used to obtain not only an approximate numerical solution, but also an approximate analytical solution when using initial conditions that come from pre-bleach steady states and also general initial conditions, to facilitate asymptotic analysis. Analytical and numerical results are presented. It is observed that although KSS methods are explicit, it is possible to use a time step that is far greater than what the CFL condition would indicate.

Comments

© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.

Publication Title

Computers & Mathematics with Application

Volume

75

Issue

6

First Page

2153

Last Page

2172

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