methods. (a) Natural continuation fails in the prese...Figure 6.6 Level curve
of Himmelblau's function (6.46). (a) Starting the s...
7 Chapter 7Figure 7.1 DFT of
. (a) Fourier coefficients
provided by Code 22. (b) Dis...Figure 7.2 Sampling process. (a) The ordinates
(gray circles) are the samp...Figure 7.3 (a) The signal
is sampled using
measurements every
time uni...Figure 7.4 Fourier differentiation of function
. (a) Sampled function at
...Figure 7.5 Exponential convergence of Fourier differentiation of function
....Figure 7.6 Differentiation of function
in Fourier space, following Figure ...
8 Chapter 8Figure 8.1 Numerical solution of (8.41) provided by the approximated linear ...Figure 8.2 Numerical solution of (8.42). (a) Graphical representation of the...Figure 8.3 Solutions of BVP (8.47). (a) First solution approximation
(whit...Figure 8.4 Eigenvalues and eigenfunctions of Mathieu's equation (8.58). (a) ...Figure 8.5 Eigenvalues and eigenfunctions of Schrödinger's equation for the ...Figure 8.6 Discretization of (8.76) on an equally spaced time grid. Only
i...Figure 8.7 Accuracy of Runge–Kutta methods RK1, RK2 and RK4. (a) Time integr...Figure 8.8 Adams method. (a) Previously computed
‐steps
. (b) Evaluation o...Figure 8.9 A BDF method is based on differentiating the interpolant
(black...Figure 8.10 Absolute global error
at
of linear multistep formulas (LMSFs...Figure 8.11 Numerical solution of
using explicit Euler method (8.83). (a) Figure 8.12 Numerical solution of
using implicit Euler method BDF1 with
....Figure 8.13 (a) Stability region of the explicit Euler method (8.158), in gr...Figure 8.14 (a) Region of absolute stability (light gray region) of Heun's R...Figure 8.15 (a) Region of absolute stability (in gray) of
‐step Adams–Bashf...Figure 8.16 (a) Instability regions of
‐step BDF2 (light gray) and
‐step B...Figure 8.17 Solution
to the IVP (8.224) starting from
(solid black). If Figure 8.18 Nonlinear system (8.236) for
and
. (a) Phase portrait showing...Figure 8.19 Numerical integration of nonlinear system (8.236) for
