Computational Science
Illustrating practical examples from computational science, this applications-oriented book teaches students and engineers how to employ mathematical techniques for simulation and data processing using Mathcad.
TABLE OF CONTENTS Computational Science
Index
A
accept-reject algorithm, 40
accuracy order, 197, 208, 374
Adams-Bashford algorithm, 189 192
advection equation, 364 367, 376
algebra, computational linear, 138
algorithm stability, 204
algorithms
See also specific algorithm or method
attractor search, 238 253
criteria for solving ODEs, 196 202
FFT (fast Fourier transform), 57 61
implicit and explicit, 186 187
predictor-corrector, 189
shooting method, 288 291
for solving ODEs, 186 189
aliasing described, 63 65
analyses
spectrum, 56 73
wavelet, 84 88
anisotropic problems, 286
approximation order, 197, 374
arrays and random numbers, 24
artificial diffusion, 377 385, 382
asymmetrical schemes, 210
attractor reconstruction, 90 91
attractors
attractor search algorithms, 238 253
of dynamical systems, 223 232
on raster graphs, 169
stability of, 253 262
types of, 232 238
auto-oscillations
described, 172, 266
and Hopf bifurcation, 270 275
and strange attractors, 281
autocorrelation function, 43, 70 71
autonomous systems, 217 218
averages, moving, 76 78
B
B-splines, 28 30
band-pass filtration, 80 81
Bezier curves and B-splines, interpolation, 28 30
bibliography, 387
bifurcations, dynamical systems, 262 267
biotic potential, 164
boundary frequency, 62
boundary-value problems, 313 324
eigenvalue problems, 291 327
Euler method, 313 318
nonlinear, 327 332
for partial differential equations (PDE), 333
problem definition, 282 288
reducing to Cauchy problems, 288 291
stiff problems and implicit schemes, 318 324
brusselator model, 220 223
buoyancy frequency, 297
Burger s equation, 369 370
C
calculating
cubic spline interpolations, 26 28
mean value and dispersion, 13 15
moving averages, 76 78
power spectrum of model data, 83
wavelet spectrums, 84 87
Cauchy problems
and Adams-Bashford algorithm, 189 192
algorithm criteria for solving ODEs, 196 202
and dynamical systems, 217 219
and explicit Euler algorithm, 175 181
formulating for ODEs, 159 168
for ODEs, 217 223
and phase space, 168 175
reducing boundary-value problems...
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