On the application of multiquadric bases in conjunction with the LTDRM method to solve nonlinear diffusion equations

DOI10.1016/S0096-3003(97)10130-8zbMath0943.65118MaRDI QIDQ1294365

Huan-Wen Liu, Song-Ping Zhu

Publication date: 29 June 1999

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

zbMATH Keywords

boundary element methodconvergence ratethin plate splinesLaplace transform dual reciprocity methodmultiquadratic basesnonlinear transient diffusion equations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace transform (44A10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (6)

A Laplace transformation dual‐reciprocity boundary element method for a class of two‐dimensional microscale thermal problems ⋮ The dual reciprocity boundary element method for magnetohydrodynamic channel flows ⋮ A Laplace transform DRBEM with a predictor-corrector scheme for time-dependent infiltration from periodic channels with root-water uptake ⋮ Axisymmetric polyharmonic spline approximation in the dual reciprocity method ⋮ A perturbation DRBEM model for weakly nonlinear wave run-ups around islands ⋮ A general DRBEM model for wave refraction and diffraction

Uses Software

• Algorithm 368

Cites Work

• Numerical inversion of the Laplace transform: a survey and comparison of methods
• Application of the Laplace transform to nonlinear transient problems
• An application of the LTDRM to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions
• A boundary element approach for nonhomogeneous potential problems
• Miscellaneous error bounds for multiquadric and related interpolators
• A boundary element approach for parabolic differential equations using a class of particular solutions
• Truncated Laurent expansions for the fast evaluation of thin plate splines
• A DRBEM model for microwave heating problems
• Recent developments in the numerical evaluation of particular solutions in the boundary element method
• An efficient computational method for modelling transient heat conduction with nonlinear source terms
• Application of the boundary element method to non-linear diffusion with reaction problems
• Local error estimates for radial basis function interpolation of scattered data
• An indirect Boundary Element Method for solving low Reynolds number Navier-Stokes equations in a three-dimensional cavity
• Improvement on dual reciprocity boundary element method for equations with convective terms
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Some comments on the use of radial basis functions in the dual reciprocity method
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