By Prof. Rubin H. Landau, Prof. Manuel J. Paez, Prof. Cristian C. Bordeianu(auth.)
This moment variation raises the universality of the former version through offering all its codes within the Java language, whose compiler and improvement equipment can be found at no cost for primarily all working structures. furthermore, the accompanying CD offers a number of the comparable codes in Fortran ninety five, Fortran seventy seven, and C, for much more common software, in addition to MPI codes for parallel functions. The booklet additionally contains new fabrics on trial-and-error seek thoughts, IEEE floating element mathematics, likelihood and records, optimization and tuning in a number of languages, parallel computing with MPI, JAMA the Java matrix library, the answer of simultaneous nonlinear equations, cubic splines, ODE eigenvalue difficulties, and Java plotting programs.
From the reports of the 1st edition:
"Landau and Paez's ebook will be a good selection for a path on computational physics which emphasizes computational equipment and programming." - American magazine of PhysicsContent:
Chapter 1 creation (pages 1–5): Chaim Potok
Chapter 2 Computing software program fundamentals (pages 7–28):
Chapter three error and Uncertainties in Computations (pages 29–43):
Chapter four Object?Oriented Programming: Kinematics? (pages 45–57):
Chapter five Integration (pages 59–73):
Chapter 6 Differentiation (pages 75–80):
Chapter 7 Trial and blunder looking (pages 81–87):
Chapter eight Matrix Computing and N?D Newton Raphson (pages 89–109):
Chapter nine info becoming (pages 111–135):
Chapter 10 Deterministic Randomness (pages 137–144):
Chapter eleven Monte Carlo purposes (pages 145–163):
Chapter 12 Thermodynamic Simulations: Ising version (pages 165–178):
Chapter thirteen laptop fundamentals: reminiscence and CPU (pages 179–187):
Chapter 14 High?Performance Computing: Profiling and Tuning (pages 189–206):
Chapter 15 Differential Equations functions (pages 207–233):
Chapter sixteen Quantum Eigenvalues through ODE Matching (pages 235–244):
Chapter 17 Fourier research of Linear and Nonlinear signs (pages 245–265):
Chapter 18 strange Dynamics of Nonlinear structures (pages 267–276):
Chapter 19 Differential Chaos in section house (pages 277–292):
Chapter 20 Fractals (pages 293–311):
Chapter 21 Parallel Computing (pages 313–320):
Chapter 22 Parallel Computing with MPI (pages 321–350):
Chapter 23 Electrostatics Potentials through Finite transformations (PDEs) (pages 351–368):
Chapter 24 warmth movement (pages 369–377):
Chapter 25 PDE Waves on Strings and Membranes (pages 379–398):
Chapter 26 Solitons; KdeV and Sine?Gordon (pages 399–415):
Chapter 27 Quantum Wave Packets? (pages 417–425):
Chapter 28 Quantum Paths for useful Integration (pages 427–441):
Chapter 29 Quantum certain States through critical Equations (pages 443–450):
Chapter 30 Quantum Scattering through critical Equations (pages 451–459):
Chapter A PtPlot: 2nd Graphs inside Java (pages 461–465):
Chapter B thesaurus (pages 467–478):
Chapter C Fortran ninety five Codes (pages 479–511):
Chapter D Fortran seventy seven Codes (pages 513–546):
Chapter E c program languageperiod Codes (pages 547–581):
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Extra resources for Computational Physics: Problem Solving with Computers, Second Edition
29) To see if these assumptions are correct, and determine what level of precision is possible for the best choice of N, you would plot log10 |( A( N ) − A(2N )/A(2N )| versus log10 N, similar to what we have done in Fig. 4. If you obtain a rapid straight-line drop off, then you know you are in the region of convergence and can deduce a value for β from the slope. As N gets larger, you should see the graph change from the previous straight line decrease to a slow increase as the roundoff error begins to dominate.
The fact that the error must fall off for large N is just a statement that the algorithm converges. In contrast to this algorithmic error, roundoff errors tend to grow slowly and somewhat randomly with N. 25) ro 39 40 3 Errors and Uncertainties in Computations Indeed this is the slow growth with N we expect from the roundoff error. 26) m We expect the first term to be the larger of the two for small N, but ultimately to be overcome by the slowly growing second term. As an example, in Fig. 4 we present a log–log plot of the relative error in numerical integration using the Simpson integration rule (Chap.
14) where the subscript c is a reminder that this is computer representation of 1. Consequently, an arbitrary number x can be thought of as related to its the floating-point representation xc by x c = x (1 ± ) | |≤ m where the actual value for is not known. 10 Determine Your Machine Precision single-precision numbers contain an error in their sixth decimal place, and that all doubles have an error in their 15th place. And as is always the case with errors, there is no way to know ahead of time what the error is, for if we could, then we would get rid of the error!