jburkardt

FEYNMAN_KAC_2D\ PDE Solution by Feynman-Kac Algorithm {#feynman_kac_2d-pde-solution-by-feynman-kac-algorithm align=”center”} =====================================

---

FEYNMAN_KAC_2D is a C++ program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson’s equation in a 2D ellipse by averaging stochastic paths to the boundary.

The program is intended as a simple demonstration of the method. The main purpose is to have a version that runs sequentially, so that it can be compared to versions which have been enhanced using parallel programming techniques.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

FEYNMAN_KAC_2D is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs: {#related-data-and-programs align=”center”}

FEYNMAN_KAC_1D, a C++ program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson’s equation in a 1D interval by averaging stochastic paths to the boundary.

FEYNMAN_KAC_3D, a C++ program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson’s equation in a 3D ellipsoid by averaging stochastic paths to the boundary.

SDE, a MATLAB library which solves certain stochastic differential equations.

STOCHASTIC_RK, a C++ library which applies a Runge-Kutta scheme to a stochastic differential equation.

Reference: {#reference align=”center”}

1. Peter Arbenz, Wesley Petersen,\ Introduction to Parallel Computing - A practical guide with examples in C,\ Oxford University Press,\ ISBN: 0-19-851576-6,\ LC: QA76.58.P47.

Source Code: {#source-code align=”center”}

• feynman_kac_2d.cpp, the source code.

Examples and Tests: {#examples-and-tests align=”center”}

• feynman_kac_2d_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• MAIN is the main program for FEYNMAN_KAC_2D.
• POTENTIAL evaluates the potential function V(X,Y).
• R8_ABS returns the absolute value of an R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

---

Last revised on 16 November 2011.