Highly accurate compact difference scheme for fourth order parabolic equation with Dirichlet and Neumann boundary conditions: Application to good Boussinesq equation
作者：
Highlights：
• Using three-spatial grid points, we have derived a new method of order two in time and four in space for 4th order quasilinear parabolic equations.
• We do not require to discretize the boundary conditions.
• The numerical solution of first order space derivative is obtained as by-product of the method.
• The proposed method is applicable to singular problems.
• We have solved single and double-soliton of good Boussinesq equations, Euler-Bernoulli beam equation, and evolution problems.
摘要
•Using three-spatial grid points, we have derived a new method of order two in time and four in space for 4th order quasilinear parabolic equations.•We do not require to discretize the boundary conditions.•The numerical solution of first order space derivative is obtained as by-product of the method.•The proposed method is applicable to singular problems.•We have solved single and double-soliton of good Boussinesq equations, Euler-Bernoulli beam equation, and evolution problems.
论文关键词：Fourth order parabolic equation,Compact difference scheme,Good Boussinesq equation,Block tridiagonal matrix,Singularity,Soliton
论文评审过程：Received 21 June 2019, Revised 22 February 2020, Accepted 5 March 2020, Available online 27 March 2020, Version of Record 27 March 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125202
