A time–efficient variable shape parameter Kansa–radial basis function method for the solution of nonlinear boundary value problems

作者：

Highlights：

• Application of a radial basis function collocation method to two-and three-dimensional nonlinear boundary value problems.

• The solution of the resulting system of nonlinear equations is achieved using the MATLAB optimization toolbox functions fsolve or lsqnonlin.

• Derivation of the analytical expression of the Jacobian of the nonlinear systems in question which leads to substantial savings in computational time.

• This enables one to solve, in addition to 2D problems, 3D second and fourth order nonlinear boundary value problems in complicated domains.

摘要

•Application of a radial basis function collocation method to two-and three-dimensional nonlinear boundary value problems.•The solution of the resulting system of nonlinear equations is achieved using the MATLAB optimization toolbox functions fsolve or lsqnonlin.•Derivation of the analytical expression of the Jacobian of the nonlinear systems in question which leads to substantial savings in computational time.•This enables one to solve, in addition to 2D problems, 3D second and fourth order nonlinear boundary value problems in complicated domains.

论文关键词：RBFs,Kansa method,Collocation,Nonlinear PDEs

论文评审过程：Received 7 March 2021, Revised 18 May 2021, Accepted 17 August 2021, Available online 31 August 2021, Version of Record 31 August 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126613