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Numerical analysis of a singularly perturbed nonlinear reaction–diffusion problem with multiple solutions

2004
*
Applied Numerical Mathematics
*

*A*

*nonlinear*reaction-

*diffusion*two-point boundary value

*problem*with multiple solutions is considered. ...

*Numerical*experiments are performed to support the theoretical results. ... This is not

*a*practical restriction, and from

*a*theoretical viewpoint the

*analysis*

*of*

*a*

*nonlinear*

*problem*such as (1.1) would be very different if ε were not small. ε ≤ CN −1 , (1. Notation. ...

##
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Finite element solution of a nonlinear diffusion problem with a moving boundary

1986
*
Mathematical Modelling and Numerical Analysis
*

et Analyse numérique
Mathematical Modelhng and Numencal

doi:10.1051/m2an/1986200304031
fatcat:er26rj422jctfdsh2yt5g4e654
*Analysis**A**NONLINEAR**DIFFUSION**PROBLEM*413 THEOREM 1 : Let the assump lions*of*lemma 1 be satisfied and let : b(w, t;v,v)^0 Vu e V(t\ te ... The underlying mathematical*problem*consists in solving*numerically*the following boundary value*problem*: Hère u is the unknown concentration*of*an impurity, D(u) is the concentration dependent*diffusion*...*A**NONLINEAR**DIFFUSION**PROBLEM*417 We introducé one more notation. If z(x, y, Q is defined on Q l we dénote by z'the function defined on Q I+1 by : ? ...##
###
Multiscale analysis and simulation of a reaction–diffusion problem with transmission conditions

2010
*
Nonlinear Analysis: Real world applications
*

Jäger Multiscale

doi:10.1016/j.nonrwa.2008.11.024
fatcat:phu345qdvbh33hxh57ebuqxybi
*analysis*and simulation*of**a*reaction-*diffusion**problem*with transmission conditions.*Nonlinear**Analysis*-RWA (2009). Electronic Version: http://dx. ...*Numerically*the*problem*is reduced to*a*system*of*ordinary differential equations, where the coupling*of*the micro-and macrovariables leads to*a*special structure, distinguishing the variables relevant ... Jäger Multiscale*analysis*and simulation*of**a*reaction-*diffusion**problem*with transmission conditions.*Nonlinear**Analysis*-RWA (2009). ...##
###
Preface

1998
*
Journal of Computational and Applied Mathematics
*

Preface This special issue is devoted to applications and

doi:10.1016/s0377-0427(98)00099-5
fatcat:emz3bhy47rcxhoe2edtwxa4w3m
*numerical**analysis**of**Nonlinear*Parabolic*Problems*with Blow-up Solutions. It is*a*subject that has experienced*a*steady growth since S. ... in the theory, applications, and the*numerical**analysis**of*blow-up*problems*. ... The remaining three papers focus on the*numerical**analysis*and the computational treatment*of*blow-up*problems*. ...##
###
Extended Forward Sensitivity Analysis for Uncertainty Quantification

2013
*
Nuclear Technology
*

Two well defined benchmark

doi:10.13182/nt13-a15766
fatcat:gvrr5ehtcjeipk6n7nmssc6ymq
*problems*, thermal wave and*nonlinear**diffusion*, are utilized to demonstrate the extended forward sensitivity*analysis*method. ... This report presents the forward sensitivity*analysis*method as*a*means for quantification*of*uncertainty in system*analysis*. ... For small , we call the*problem**a*weak*nonlinear**diffusion**problem*; and for large , i.e., =7, we call it*a*strong*nonlinear**diffusion**problem*. ...##
###
Author index volume 97 (1998)

1998
*
Journal of Computational and Applied Mathematics
*

*Numerical*

*analysis*

*of*radially nonsymmetric blow-up solutions

*of*

*a*

*nonlinear*parabolic

*problem*Galaktionov, V.A., see Budd, C.J. 51-80 51-80 81-97 51-80 Herrero, M.A., E. Medina and J.J.L. ... ., Difference schemes

*of*optimum degree

*of*implicitness for

*a*family

*of*simple ODEs with blow-up solutions Roberts, C.A.,

*Analysis*

*of*explosion for

*nonlinear*Volterra equations Sloan, D.M., see Brunner ... Vasileva,

*Numerical*

*analysis*

*of*radially nonsymmetric blow-up solutions

*of*

*a*

*nonlinear*parabolic

*problem*Galaktionov, V.A., see Budd, C.J. M.A., E. Medina and J.J.L. ...

##
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Page 837 of Mathematical Reviews Vol. , Issue 82b
[page]

1982
*
Mathematical Reviews
*

The paper contains

*a*formulation*of*the*problem**of*one-dimensional*diffusion**of**a*single impurity in semiconductors, and the result*of**numerical*computation describing the*diffusion**of*boron in silicon ... We illustrate the operation*of*the program using the example*of*adiabatic absorption.” Hogge, M.*A*. 82b:80007 Secant versus tangent methods in*nonlinear*heat transfer*analysis*. Internat. J.*Numer*. ...##
###
Page 3432 of Mathematical Reviews Vol. , Issue 99e
[page]

1999
*
Mathematical Reviews
*

99e:65135
element method for

*diffusion**problems*is presented in the format*of**a*sequence. ... The*numerical*results show the advantages*of*such*a*method.” 99e:65136 65M70 35A25 35Q53 Fokas,*A*. S. (4-LNDIC; London) Lax pairs and*a*new spectral method for linear and integrable*nonlinear*PDEs. ...##
###
Uniform Convergence of a Monotone Iterative Method for a Nonlinear Reaction-Diffusion Problem
[chapter]

2005
*
Lecture Notes in Computer Science
*

*a*mixer p. 598 Stability

*analysis*

*of*

*a*

*nonlinear*model

*of*wastewater treatment processes p. 606

*Numerical*search for the states with minimal dispersion in quantum mechanics with non-negative quantum distribution ...

*of*Si

*diffusion*in Fe substrates after hot dipping and

*diffusion*annealing p. 399

*Numerical*design

*of*optimal active control for seismically-excited building structures p. 408 Computing transitive ...

##
###
Page 741 of Mathematical Reviews Vol. , Issue 84b
[page]

1984
*
Mathematical Reviews
*

In the development

*of**a**numerical*algorithm for*nonlinear*partial differential equations, linear*analysis*is often used to guide the choice*of*discretization schemes and solution methods. ... He points out, and illustrates through two examples, how*a*simple linear*analysis*can fail for general*nonlinear**problems*. {For the entire collection see MR 83k:00004. } Murli M. ...##
###
Page 5184 of Mathematical Reviews Vol. , Issue 2002G
[page]

2002
*
Mathematical Reviews
*

Summary: “This paper is devoted to

*a**numerical**analysis**of*pe- riodic solutions*of**a*finite difference system which is*a*discrete version*of**a*class*of**nonlinear*reaction-*diffusion*-convection equa- tions ... Also given are some*numerical*results*of**a*logistic reaction-*diffusion**problem*.” 2002g:65109 65M06 35Q30 Shapeey,*A*. V. ...##
###
Homotopy analysis method for solving nonlinear diffusion equation with convection term

2014
*
International Journal of Applied Mathematical Research
*

In this article the homotopy

doi:10.14419/ijamr.v3i3.2899
fatcat:xcttjcf5rfdvdawlslbesqbpee
*analysis*method (HAM) is used to find*a**numerical*solution for the*nonlinear**diffusion*equation with convection term. ... The*numerical*results obtained by using this method compared with the exact solution, by solving*numerical*example shows that (HAM) is accurate and close to the exact solution. ... Apart*of**a*limited number*of*these*problems*, most*of*them do not have*a*precise analytical solution, so these*nonlinear*equations should be solved using approximate methods. ...##
###
Review of trends in theory and practice of nonlinear differential equations, lecture notes in pure and applied mathematics

1986
*
Computers and Mathematics with Applications
*

differential equations, shockless airfoils, singular perturbations

doi:10.1016/0898-1221(86)90186-0
fatcat:dwlcprpb7nhn3dlp7mohlk6u6a
*of**nonlinear*elliptic boundary value*problems*, three-dimensional*nonlinear*evolution*of*water waves,*numerical*solution*of*two-dimensional ... computation*of*capillary-gravity waves, integrable*nonlinear*field theories,*numerical*solution*of*stationary Navier-Stokes equations, similarity solutions*of*evolution equations, solutions for*a*finite ... differential equations, shockless airfoils, singular perturbations*of**nonlinear*elliptic boundary value*problems*, three-dimensional*nonlinear*evolution*of*water waves,*numerical*solution*of*two-dimensional ...##
###
Review of nonlinear partial differential equations in engineering and applied science, lecture notes in pure and applied mathematics

1986
*
Computers and Mathematics with Applications
*

differential equations, shockless airfoils, singular perturbations

doi:10.1016/0898-1221(86)90187-2
fatcat:han24dvvqnfzbdr5hq4r42tcna
*of**nonlinear*elliptic boundary value*problems*, three-dimensional*nonlinear*evolution*of*water waves,*numerical*solution*of*two-dimensional ... computation*of*capillary-gravity waves, integrable*nonlinear*field theories,*numerical*solution*of*stationary Navier-Stokes equations, similarity solutions*of*evolution equations, solutions for*a*finite ... differential equations, shockless airfoils, singular perturbations*of**nonlinear*elliptic boundary value*problems*, three-dimensional*nonlinear*evolution*of*water waves,*numerical*solution*of*two-dimensional ...##
###
Page 4998 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

This work is

*a*substantial contribution in the field*of**numerical**analysis*applied to*a*class*of**problems*which is important from the point*of*view*of*applications. ... This*problem*occurs in many mathematical models*of*physical processes: for example,*nonlinear**diffusion*and filtration and non-Newtonian flows. ...
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