# NAG Library Chapter Contents

## D03 (pde)Partial Differential Equations

D03 (pde) Chapter Introduction – a description of the Chapter and an overview of the algorithms available

 RoutineName Mark ofIntroduction Purpose d03eaf Example Text Example Data 7 nagf_pde_dim2_laplace Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain d03ebf Example Text Example DataExample Plot 7 nagf_pde_dim2_ellip_fd Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence d03ecf Example Text Example DataExample Plot 8 nagf_pde_dim3_ellip_fd Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence d03edf Example Text Example DataExample Plot 12 nagf_pde_dim2_ellip_mgrid Elliptic PDE, solution of finite difference equations by a multigrid technique d03eef Example Text Example DataExample Plot 13 nagf_pde_dim2_ellip_discret Discretize a second-order elliptic PDE on a rectangle d03faf Example Text Example Data 14 nagf_pde_dim3_ellip_helmholtz Elliptic PDE, Helmholtz equation, three-dimensional Cartesian coordinates d03maf Example Text Example DataExample Plot 7 nagf_pde_dim2_triangulate Triangulation of plane region d03ncf Example Text Example DataExample Plot 20 nagf_pde_dim1_blackscholes_fd Finite difference solution of the Black–Scholes equations d03ndf Example Text Example DataExample Plot 20 nagf_pde_dim1_blackscholes_closed Analytic solution of the Black–Scholes equations d03nef Example Text Example DataExample Plot 20 nagf_pde_dim1_blackscholes_means Compute average values for d03ndf d03pcaExample TextExample DataExample Plot 20 nagf_pde_1d_parab_fd General system of parabolic PDEs, method of lines, finite differences, one space variable d03pcf Example Text Example DataExample Plot 15 nagf_pde_dim1_parab_fd_old General system of parabolic PDEs, method of lines, finite differences, one space variable d03pdaExample TextExample DataExample Plot 20 nagf_pde_1d_parab_coll General system of parabolic PDEs, method of lines, Chebyshev ${C}^{0}$ collocation, one space variable d03pdf Example Text Example DataExample Plot 15 nagf_pde_dim1_parab_coll_old General system of parabolic PDEs, method of lines, Chebyshev ${C}^{0}$ collocation, one space variable d03pef Example Text Example DataExample Plot 16 nagf_pde_dim1_parab_keller General system of first-order PDEs, method of lines, Keller box discretization, one space variable d03pff Example Text Example Data 17 nagf_pde_dim1_parab_convdiff General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable d03phaExample TextExample DataExample Plot 20 nagf_pde_1d_parab_dae_fd General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable d03phf Example Text Example DataExample Plot 15 nagf_pde_dim1_parab_dae_fd_old General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable d03pjaExample TextExample DataExample Plot 20 nagf_pde_1d_parab_dae_coll General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev ${C}^{0}$ collocation, one space variable d03pjf Example Text Example DataExample Plot 15 nagf_pde_dim1_parab_dae_coll_old General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev ${C}^{0}$ collocation, one space variable d03pkf Example Text Example DataExample Plot 16 nagf_pde_dim1_parab_dae_keller General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, one space variable d03plf Example Text Example DataExample Plot 17 nagf_pde_dim1_parab_convdiff_dae General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable d03ppaExample TextExample DataExample Plot 20 nagf_pde_1d_parab_remesh_fd General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable d03ppf Example Text Example DataExample Plot 16 nagf_pde_dim1_parab_remesh_fd_old General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable d03prf Example Text Example DataExample Plot 16 nagf_pde_dim1_parab_remesh_keller General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretization, remeshing, one space variable d03psf Example Text Example DataExample Plot 17 nagf_pde_dim1_parab_convdiff_remesh General system of convection-diffusion PDEs, coupled DAEs, method of lines, upwind scheme, remeshing, one space variable d03puf 17 nagf_pde_dim1_parab_euler_roe Roe's approximate Riemann solver for Euler equations in conservative form, for use with d03pff, d03plf and d03psf d03pvf 17 nagf_pde_dim1_parab_euler_osher Osher's approximate Riemann solver for Euler equations in conservative form, for use with d03pff, d03plf and d03psf d03pwf Example Text Example DataExample Plot 18 nagf_pde_dim1_parab_euler_hll Modified HLL Riemann solver for Euler equations in conservative form, for use with d03pff, d03plf and d03psf d03pxf Example Text Example DataExample Plot 18 nagf_pde_dim1_parab_euler_exact Exact Riemann solver for Euler equations in conservative form, for use with d03pff, d03plf and d03psf d03pyf 15 nagf_pde_dim1_parab_coll_interp PDEs, spatial interpolation with d03pdf/d03pda or d03pjf/d03pja d03pzf 15 nagf_pde_dim1_parab_fd_interp PDEs, spatial interpolation with d03pcf/d03pca, d03pef, d03pff, d03phf/d03pha, d03pkf, d03plf, d03ppf/d03ppa, d03prf or d03psf d03raf Example Text Example DataExample Plot 18 nagf_pde_dim2_gen_order2_rectangle General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region d03rbf Example Text Example Data 18 nagf_pde_dim2_gen_order2_rectilinear General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region d03ryf 18 nagf_pde_withdraw_2d_gen_order2_checkgrid Check initial grid data in d03rbfNote: this routine is scheduled for withdrawal at Mark 27, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. d03rzf 18 nagf_pde_dim2_gen_order2_rectilinear_extractgrid Extract grid data from d03rbf d03uaf Example Text Example DataExample Plot 7 nagf_pde_dim2_ellip_fd_iter Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration d03ubf Example Text Example DataExample Plot 8 nagf_pde_dim3_ellip_fd_iter Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration