首页|The Method of Polynomial Particular Solutions for Solving Nonlinear Poisson-Type Equations

The Method of Polynomial Particular Solutions for Solving Nonlinear Poisson-Type Equations

扫码查看
原文链接
  • NETL
  • NSTL
  • 万方数据
In this paper,the method of polynomial particular solutions is used to solve nonlinear Poisson-type partial differential equations in one,two,and three dimensions.The condition number of the coefficient matrix is reduced through the implementation of multiple scale technique,ultimately yielding a stable numerical solution.The methodological process can be divided into two main parts:first,identifying the corresponding polynomial particular solutions for the linear differential operator terms in the governing equations,and second,employing these polynomial particular solutions as basis function to iteratively solve the remaining nonlinear terms within the governing equations.Additionally,we investigate the potential improvement in numerical accuracy for equations with singularities in the analytical solution by shifting the computational domain a certain distance.Numerical experiments are conducted to assess both the accuracy and stability of the proposed method.A comparison of the obtained results with those produced by other numerical methods demonstrates the accuracy,stability,and efficiency of the proposed method in handling nonlinear Poisson-type partial differential equations.

Nonlinear equationSingularityPolynomial particular solutionsPoisson type

Zhile Jia、Yanhua Cao、Xiaoran Wu

展开 >

School of Sciences,East China Jiaotong University,Nanchang 330013,China

science and Technology Research Project of Education Department of Jiangxi ProvincePhilippine Council for Industry,Energy,and Emerging Technology Research and DevelopmentNational Natural Science Foundation of ChinaJiangxi Provincial Natural Science Foundation

GJJ22006051146102620282BA8201016

2024

10.1007/s10338-023-00440-w

固体力学学报(英文版)
中国力学学会

固体力学学报(英文版)

EI
影响因子：0.214
ISSN：0894-9166
年,卷(期)：2024.37(1)
  • 29