Codes4book

Computer Codes for Applied Numerical Methods for Partial Differential Equations by Carl L. Gardner, Springer (November 2024)

Email comments to carl.gardner@asu.edu

The computer programs are all self-contained for simplicity of use. For example, chd.m has a built-in WENO3 solver identical to the one in weno3.m

The WENO3 solver was developed by Jeremiah Jones and Carl Gardner, SoMSS, Arizona State University

Errata, Clarifications, & Additional Material for the Book are in the file errata.pdf

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burgers1.m conservative upwind method and four versions of the Lax-Friedrichs method for the inviscid Burgers equation

burgers3.m WENO3 method for the inviscid Burgers equation

bvp.m solves a linear BVP using central differences and a tridiagonal direct solve

chd.m WENO3 method for the classical hydrodynamic model for semiconductor devices

diffusion0.m backward Euler method for the linear diffusion equation with fixed timestep and Dirichlet BCs

diffusion1.m TRBDF2 method for the linear diffusion equation with fixed timestep and Dirichlet BCs

diffusion2.m TRBDF2 method for the linear diffusion equation with dynamic timestep and Dirichlet BCs

diffusionNBC.m TRBDF2 method for the linear diffusion equation with dynamic timestep and homogeneous Neumann BCs

diffusion2D.m TRBDF2 method for the 2D linear diffusion equation with fixed timestep for movie and Dirichlet BCs

ivp.m solves the IVP 𝑑𝑦/𝑑𝑡 = −𝑦, 𝑦(0) = 𝑦0, using forward Euler, backward Euler, and TR

jets.m simulates 2D gas dynamical supersonic jets using the WENO3 method

laplace0.m banded matrix direct solve for the 2D Laplace equation with Dirichlet BCs

laplace1.m Jacobi iteration for the 2D Laplace equation with Dirichlet BCs

laplace2.m Gauss-Seidel iteration for the 2D Laplace equation with Dirichlet BCs

laplace3.m SOR iteration for the 2D Laplace equation with Dirichlet BCs

laplace4.m conjugate gradient method for the 2D Laplace equation with Dirichlet BCs

laplace5.m PCG method for the 2D Laplace equation with Dirichlet BCs

laplace6.m MATLAB built-in CG, PCG, or GMRES method for the 2D Laplace equation with Dirichlet BCs

laplaceNBC.m SOR method for the 2D Laplace equation with a Neumann BC on one side

layer.m solves the nonlinear layer BVP using central differences by Newton iteration (with a tridiagonal direct solve)

lorenz1.m solves the Lorenz equations using fourth/fifth-order Runge-Kutta or TRBDF2

lorenz2.m solves the Lorenz equations with two different sets of initial conditions using fourth/fifth-order Runge-Kutta

lorenz3.m solves the Lorenz equations with three different methods or sets of initial conditions using fourth/fifth-order Runge-Kutta

lorenzeigs.m calculates the eigenvalues of the Lorenz Jacobian at the equilibria of the Lorenz equations

nonlin_diffusion.m solves the nonlinear diffusion equation with homogeneous Neumann BCs using TRBDF2 with dynamic timestep and Newton’s method

nonlin_laplace.m solves the 2D nonlinear Laplace equation with Dirichlet BCs using Newton’s method with a banded matrix direct solve or GMRES

pendulum.m plots the phase space diagram/direction field for the nonlinear pendulum

rk2.m solves the IVP 𝑑𝑤/𝑑𝑡 = 𝑓(𝑤) using second-order Runge-Kutta with fixed timestep

rk2dyn.m solves the IVP 𝑑𝑤/𝑑𝑡 = 𝑓(𝑤) using second-order Runge-Kutta with dynamic timestep

shaw.m solves the Shaw equations using fourth/fifth-order Runge-Kutta

wave1.m solves the first-order wave equation using the original upwind method

wave2.m solves the second-order wave equation as a first-order system using the Lax-Friedrichs or Lax-Wendroff method

wave3.m solves the first-order wave equation using the WENO3 method

weno3.m solves 1D gas dynamical Riemann problems using the WENO3 method with Lax-Friedrichs flux splitting