Filters








160,721 Hits in 5.0 sec

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

Natalia Kopteva, Martin Stynes
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.  ... 
doi:10.1016/j.apnum.2004.07.001 fatcat:shfqbbgfhfhf3i42osgdromoai

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

Libor Čermák, Miloš Zlámal
1986 Mathematical Modelling and Numerical Analysis  
et Analyse numérique Mathematical Modelhng and Numencal 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 : ?  ... 
doi:10.1051/m2an/1986200304031 fatcat:er26rj422jctfdsh2yt5g4e654

Multiscale analysis and simulation of a reaction–diffusion problem with transmission conditions

Maria Neuss-Radu, Stephan Ludwig, Willi Jäger
2010 Nonlinear Analysis: Real world applications  
Jäger Multiscale 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).  ... 
doi:10.1016/j.nonrwa.2008.11.024 fatcat:phu345qdvbh33hxh57ebuqxybi

Preface

Hermann Brunner, Chris J. Budd, David M. Sloan
1998 Journal of Computational and Applied Mathematics  
Preface This special issue is devoted to applications and 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.  ... 
doi:10.1016/s0377-0427(98)00099-5 fatcat:emz3bhy47rcxhoe2edtwxa4w3m

Extended Forward Sensitivity Analysis for Uncertainty Quantification

Haihua Zhao, Vincent A. Mousseau
2013 Nuclear Technology  
Two well defined benchmark 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.  ... 
doi:10.13182/nt13-a15766 fatcat:gvrr5ehtcjeipk6n7nmssc6ymq

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.  ... 
doi:10.1016/s0377-0427(98)00182-4 fatcat:sfibad4cbvau7puyd5kk73ikua

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]

Igor Boglaev
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  ... 
doi:10.1007/978-3-540-31852-1_1 fatcat:i32tc6ennffk3jrjgvbnjz2kwq

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

Bewar Mahmood, Saad A. Manaa, Fadhil H. Easif
2014 International Journal of Applied Mathematical Research  
In this article the homotopy 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.  ... 
doi:10.14419/ijamr.v3i3.2899 fatcat:xcttjcf5rfdvdawlslbesqbpee

Review of trends in theory and practice of nonlinear differential equations, lecture notes in pure and applied mathematics

Glenn Webb
1986 Computers and Mathematics with Applications  
differential equations, shockless airfoils, singular perturbations 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  ... 
doi:10.1016/0898-1221(86)90186-0 fatcat:dwlcprpb7nhn3dlp7mohlk6u6a

Review of nonlinear partial differential equations in engineering and applied science, lecture notes in pure and applied mathematics

Kevin P. Meade
1986 Computers and Mathematics with Applications  
differential equations, shockless airfoils, singular perturbations 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  ... 
doi:10.1016/0898-1221(86)90187-2 fatcat:han24dvvqnfzbdr5hq4r42tcna

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.  ... 
« Previous Showing results 1 — 15 out of 160,721 results