nag_pde_parab_1d_fd_ode (d03phc) integrates the system of parabolic-elliptic equations and coupled ODEs

nag_pde_parab_1d_fd_ode (d03phc) integrates a system of linear or nonlinear parabolic partial differential equations (PDEs) in one space variable, with scope for coupled ordinary differential equations (ODEs). The spatial discretisation is performed using finite differences, and the method of lines is employed to reduce the PDEs to a system of ODEs. The resulting system is solved using a backward differentiation formula method or a Theta method (switching between Newton’s method and functional iteration).