FD1D_BVP, a C++ program which applies the finite difference method to solve a two point boundary value problem in one spatial dimension.
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The boundary value problem (BVP) that is to be solved has the form: in the interval X[0] < x < X[N-1]. The functions a(x), c(x), and f(x) are given functions, and a formula for a'(x) is also available. Good times sam cooke download.
Traktor pro 2 cracked torrent mac. Boundary conditions are applied at the endpoints, and in this case, these are assumed to have the form:
To compute a finite difference approximation, a set of n nodes is defined over the interval, and, at each interior node, a discretized version of the BVP is written, with u'(x) and u'(x) approximated by central differences.
Usage:
fd1d_bvp ( n, a, aprime, c, f, x, u )where
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- n the number of nodes.
- a the function which evaluates a(x);
- aprime the function which evaluates a'(x);
- c the function which evaluates c(x);
- f the function which evaluates f(x).
- x the vector of n nodes, which may be nonuniformly spaced.
- u the output vector of solution values at the nodes.
Licensing:
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The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
Languages:
fd1d_bvp is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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Reference:
- Dianne O'Leary,
Finite Differences and Finite Elements: Getting to Know You,
Computing in Science and Engineering,
Volume 7, Number 3, May/June 2005. - Dianne O'Leary,
Scientific Computing with Case Studies,
SIAM, 2008,
ISBN13: 978-0-898716-66-5,
LC: QA401.O44. - Hans Rudolf Schwarz,
Finite Element Methods,
Academic Press, 1988,
ISBN: 0126330107,
LC: TA347.F5.S3313. - Gilbert Strang, George Fix,
An Analysis of the Finite Element Method,
Cambridge, 1973,
ISBN: 096140888X,
LC: TA335.S77. - Olgierd Zienkiewicz,
The Finite Element Method,
Sixth Edition,
Butterworth-Heinemann, 2005,
ISBN: 0750663200,
LC: TA640.2.Z54
Source Code:
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- fd1d_bvp.cpp, the source code.
- fd1d_bvp.sh, compiles the source code.
- fd1d_bvp.hpp, the include file.