Numerical experiments with the Bratu equation in one, two and three dimensions

DOI10.1007/s40314-013-0007-9zbMath1272.65087OpenAlexW2039537559WikidataQ59303812 ScholiaQ59303812MaRDI QIDQ361977

Janusz Karkowski

Publication date: 20 August 2013

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-013-0007-9

zbMATH Keywords

finite difference methodpseudospectral methodnumerical examplesnonlinear eigenvalue problembifurcation problemnonlinear Bratu equationradial basis functions method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Bifurcations in context of PDEs (35B32)

Related Items (7)

Block hybrid third derivative Nyström type method for Bratu's equation ⋮ Unnamed Item ⋮ On the accurate discretization of a highly nonlinear boundary value problem ⋮ A numerical study of the higher-dimensional Gelfand-Bratu model ⋮ Numerical solutions of time-fractional coupled viscous Burgers' equations using meshfree spectral method ⋮ Truncation method with point transformation for exact solution of Liouville Bratu Gelfand equation ⋮ Numerical solutions of Gelfand equation in steady combustion process

Cites Work

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• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Numerical experiments on the condition number of the interpolation matrices for radial basis functions
• One-point pseudospectral collocation for the one-dimensional Bratu equation
• Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval
• The Lie-group shooting method for solving the Bratu equation
• Exp-function method for solving nonlinear evolution equations
• A pseudo-spectral solution of 2-parameter Bratu's equation
• An efficient method for fourth-order boundary value problems
• Error saturation in Gaussian radial basis functions on a finite interval
• An analytical and numerical study of the two-dimensional Bratu equation
• Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary
• Mathematical problems from combustion theory
• Variational iteration technique for solving higher order boundary value problems
• Adomian decomposition method for a reliable treatment of the Bratu-type equations
• An efficient method for solving Bratu equations
• Barycentric Lagrange Interpolation
• Investigations of nonstandard, Mickens-type, finite-difference schemes for singular boundary value problems in cylindrical or spherical coordinates

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