poisson_1d


poisson_1d, a C code which solves a discretized version of the Poisson equation -uxx = f(x) on the interval a ≤ x ≤ b, with Dirichlet boundary conditions u(a) = ua, u(b) = ub. The linear system is solved using Gauss-Seidel iteration.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

poisson_1d is available in a C version and a FreeFem++ version and a Python version.

Related Data and Programs:

poisson_1d_test

cg_rc, a C code which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication.

cyclic_reduction, a C code which solves a tridiagonal linear system using cyclic reduction.

fd1d_bvp, a C code which applies the finite difference method to a two point boundary value problem in one spatial dimension.

gauss_seidel, a C code which uses the Gauss-Seidel iteration to solve a linear system with a symmetric positive definite (SPD) matrix.

jacobi, a C code which uses the Jacobi iteration to solving a system of linear equations with a symmetric positive definite (SPD) matrix.

mgmres, a C code which applies the restarted GMRES algorithm to solve a sparse linear system, by Lili Ju.

poisson_1d_multigrid, a C code which applies the multigrid method to a discretized version of the 1D Poisson equation.

poisson_2d, a C code which computes an approximate solution to the Poisson equation in a rectangle, using the finite difference method (FDM) and Jacobi iteration.

sor, a C code which implements the successive over-relaxation (SOR) method for the iterative solution of a linear system of equations.

Reference:

  1. William Hager,
    Applied Numerical Linear Algebra,
    Prentice-Hall, 1988,
    ISBN13: 978-0130412942,
    LC: QA184.H33.

Source Code:


Last revised on 01 October 2024.