The LMAPS for Solving Fourth-Order PDEs With Polynomial Basis Functions
Mathematics and Natural Sciences
© 2020 International Association for Mathematics and Computers in Simulation (IMACS) Due to certain difficulties in solving fourth-order partial differential equations (PDEs) using localized methods, the given differential equation is normally split into two decoupled second order PDEs. Such an approach is only feasible for Dirichlet and Laplace boundary conditions. In this paper the localized method of particular solutions is applied to fourth-order PDEs directly using polynomial basis functions. The effectiveness of the proposed algorithms is demonstrated by considering four numerical examples.
Mathematics and Computers in Simulation
(2020). The LMAPS for Solving Fourth-Order PDEs With Polynomial Basis Functions. Mathematics and Computers in Simulation, 177, 500-515.
Available at: https://aquila.usm.edu/fac_pubs/17844