摘要
In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.
基金
supported by the Key Laboratory of Road Construction Technology and Equipment(Chang’an University,No.300102253502)
the Natural Science Foundation of Shandong Province of China(GrantNo.ZR2022YQ06)
the Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province(Grant No.2022KJ140).