Simulation of the oxygen distribution in a tumor tissue using residual algorithms
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2015, Vol 3, Issue 1
Abstract
In this paper the use of recent residual algorithms for the simulation of the oxygen distribution in a tumor tissue in 2-D is proposed. The oxygen distribution in a tumor is considered a reaction-diffusion problem in steady state, whose mathematical model is a nonlinear partial differential equation, which is numerically solved using the traditional methods for systems of nonlinear equations (Newton's method, Broyden method, inexact Newton methods, etc.). Unlike of these traditional methods that require the use of derivatives and a large memory storage capacity, the proposed residual algorithms are derivative-free methods with low memory storage. The preliminary numerical results indicate that the proposed methods allows efficiently determine the distribution of oxygen in a tumor tissue to synthetic problems.
Authors and Affiliations
William La Cruz
Keywords
Related Articles
- EP ID EP240524
- DOI -
- Views 123
- Downloads 0
Loop topological complexity
We introduce here the notion of loop motion planning algorithms and show that it yields to a homotopical invariant: the loop topological complexity, denoted throughout this paper by $\rm{TC}^{\rm{LP}}(-)$, which measures...
Modeling seismic wave propagation using staggered-grid mimetic finite differences
Mimetic finite difference (MFD) approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral...
A positive spectral gradient-like method for large-scale nonlinear monotone equations
In this work, we proposed a combine form of a positive spectral gradient-like method and projection method for solving nonlinear monotone equations. The spectral gradient-like coefficient is obtained using a convex combi...
On solution of a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation by straight-line methods
We consider a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation. For this problem we prove the unique solvability in Sobolev's spaces and the maximum principle under some natural c...
Uniform Stability and Boundedness of a Kind of Third Order Delay Differential Equations
By constructing a Lyapunov functional, we obtain some sufficient conditions which guarantee the stability and boundedness of solutions for some nonlinear differential equations of third order with delay. Our results impr...