Analysis and numerical simulation of positive and dead-core solutions of singular two-point boundary value problems

DOI10.1016/j.camwa.2008.03.029zbMath1152.34320OpenAlexW2010920594MaRDI QIDQ2519528

Gernot Pulverer, Svatoslav Staněk, Ewa B. Weinmüller

Publication date: 26 January 2009

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.03.029

zbMATH Keywords

existencemultiplicityuniquenesscollocation methodspositive solutiondead-coresingular Dirichlet boundary value problemdead-core solutionpseudo-dead-core solution

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18)

Related Items (7)

Detection of dead cores for reaction-diffusion equations with a non-smooth nonlinearity ⋮ Positive and dead core solutions of singular BVPs for third-order differential equations ⋮ Analysis and numerical solutions of positive and dead core solutions of singular Sturm-Liouville problems ⋮ On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity ⋮ On singular BVPs with nonsmooth data: analysis of the linear case with variable coefficient matrix ⋮ Positive and dead-core solutions of two-point singular boundary value problems with \(\varphi \)-Laplacian ⋮ Caccioppoli-type estimates and Hardy-type inequalities derived from weighted \(p\)-harmonic problems

Uses Software

• Matlab
• bvpsuite
• Sbvp

Cites Work

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• On a singular boundary value problem arising in the theory of shallow membrane caps
• Behavior of solutions for a Robin problem
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• Approach to a dead core for some reaction-diffusion equations
• Singular reaction-diffusion boundary value problems
• A collocation code for singular boundary value problems in ordinary differential equations
• Efficient mesh selection for collocation methods applied to singular BVPs
• Efficient collocation schemes for singular boundary value problems
• Efficient numerical solution of the density profile equation in hydrodynamics
• Positive and dead core solutions of singular Dirichlet boundary value problems with \(\varphi\)-Laplacian
• From nonlinear PDEs to singular ODEs
• Computation of self-similar solution profiles for the nonlinear Schrödinger equation
• Numerical Treatment of Singular BVPs: The New MATLAB Code bvpsuite

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