Approximation of nonlinear stochastic partial differential equations by a kernel-based collocation method

DOI10.1504/IJANS.2014.061018zbMath1330.65019OpenAlexW2023364597MaRDI QIDQ902964

Qi Ye

Publication date: 4 January 2016

Published in: International Journal of Applied Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1504/ijans.2014.061018

zbMATH Keywords

convergenceKlein-Gordon equationreproducing kernelnumerical experimentGaussian fieldMatérn functionnonlinear stochastic partial differential equationskernel-based collocation methodmeshfree approximation methodSobolev-spline kernel

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) PDEs in connection with quantum mechanics (35Q40) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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The kernel regularized learning algorithm for solving Laplace equation with Dirichlet boundary ⋮ The modified dual reciprocity boundary elements method and its application for solving stochastic partial differential equations ⋮ Numerical solution of time-dependent stochastic partial differential equations using RBF partition of unity collocation method based on finite difference ⋮ Kernel-Based Approximation Methods for Partial Differential Equations: Deterministic or Stochastic Problems? ⋮ A meshless method based on the dual reciprocity method for one-dimensional stochastic partial differential equations

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