Alvaro Meseguer - Fundamentals of Numerical Mathematics for Physicists and Engineers

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 and . (...

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