
Figure 2.1 (page 106):
Dynamical regimes for the planar system dx/dt = Ax, A \in \mathbb {R}^{2 x2}.

 

Figure 2.2 (page 107):
Dynamical behavior on the region boundaries for the planar system dx/dt = Ax, A \in \mathbb {R}^{2 x2}.

 

Figure 2.4 (page 127):
Function f(x)=\exp \big (8\big (\frac {x}{\pi }\big )^{2}\big ) and truncated trigonometric Fourier series approximations with K=2,5,10. The approximations with K=5 and K=10 are visually indistinguishable from the exact function.

 

Figure 2.5 (page 128):
Truncated trigonometric Fourier series approximation to f(x)=x, using K=5,10, 50. The wiggles get finer as K increases.

 

Figure 2.6 (page 130):
Function f(x)=\exp \big (8x^{2}\big ) and truncated LegendreFourier series approximations with n=2,5,10.

 

Figure 2.7 (page 131):
Function f(x)=H(x) and truncated LegendreFourier series approximations with n=10,50,100.

 

Figure 2.12 (page 176):
Leadingorder inner U_0, outer u_0, and composite solutions u_{0c}, for Example \ref {ex:rxequil} with \epsilon =0.2, K=1, and k_{2}=1.

 

Figure 2.15 (page 187):
Contours of an energy function V(x_{1},x_{2}) or H(x_{1},x_{2}).

 

Figure 2.16 (page 191):
Energy landscape for a pendulum; H = \frac {1}{2} p^2 \kappa \cos q; \kappa =2.

 

Figure 2.17 (page 192):
Landscape for H=\frac {1}{2}p^{2}+\frac {1}{4}q^{4}\frac {1}{2}q^{2}.

 

Figure 2.18 (page 194):
A limit cycle (thick dashed curve) and a trajectory (thin solid curve) approaching it.

 

Figure 2.19 (page 195):
Periodic (left) and quasiperiodic (right) orbits on the surface of a torus. The orbit on the right eventually passes through every point in the domain.

 

Figure 2.20 (page 197):
A limit cycle for the R\"ossler system, a=b=0.2, c=1.

 

Figure 2.21 (page 197):
A strange attractor for the R\"ossler system, a=b=0.2, c=5.7.

 

Figure 2.22 (page 199):
Bifurcation diagram for the saddlenode bifurcation.

 

Figure 2.23 (page 200):
Bifurcation diagram for the transcritical bifurcation.

 

Figure 2.24 (page 201):
Bifurcation diagrams for the pitchfork bifurcation.

 

Figure 2.25 (page 206):
Approximate solutions to \dot {x}=x using explicit and implicit Euler methods with \Delta t=2.1, along with the exact solution x(t)=e^{t}.

 

Figure 2.26 (page 210):
Stability regions for AdamsBashforth methods; \dot {x}=\lambda x.

 

Figure 2.27 (page 211):
Stability regions for Adams predictorcorrector methods; \dot {x}=\lambda x.

 

Figure 2.28 (page 212):
Stability regions for RungeKutta methods; \dot {x}=\lambda x.

 

Figure 2.29 (page 214):
Hat functions for N=2.

 

Figure 2.30 (page 216):
Approximate solutions to \eqref {eq:MWRexample} using the finite element method with hat functions for N=6 and N=12. The exact solution also is shown.

 

Figure 2.31 (page 220):
Dependence of \left  c(j) \right  on j for the LegendreGalerkin approximation of \eqref {eq:MWRexample} with n=10.

 

Figure 2.34 (page 242):
Stability regions for Adams predictorcorrector methods; \dot {x}= \lambda x; APCn' uses nthorder predictor and nthorder corrector.

 


