2.1 The file Core.txt 15
2.2 The file CoreFunctions.txt 18
4.1 Listing for Taylor series expansion 57
4.2 Listing for Fourier series expansion of periodic functions 67
4.3 Listing for Fourier series expansion of nonperiodic functions 75
6.1 Listing for the digital diffusion experiment 129
8.1 Listing for the wave equation 224
16.1 Listing for the profile of elliptical Poiseuille flows 325
16.2 Listing for the mechanics of the tube flow 330
16.3 Listing for calculating flow profiles in rectangular channels 343
18.1 Listing for the time-dependent Couette flow 379
18.2 Listing for the time-dependent Hagen-Poiseuille flow 385
18.3 Listing for the time-dependent flow in rectangular cross-sections 392
19.1 Listing for Taylor-Aris dispersion 415
24.1 Listing for the contour of a sessile drop 483
24.2 Listing for the contour of a pendant drop 489
25.1 Listing for the Jacobi method 511
25.2 Listing for the Gauß-Seidel method 513
25.3 Listing for the successive over-relaxation method 515
25.4 Listing for the successive over-relaxation method with pivoting 516
25.5 Listing for LU-decomposition 522
25.6 Listing for LU-substitution without pivoting 524
25.7 Listing for LU-decomposition with pivoting 525
25.8 Listing for LU-substitution with pivoting 526
25.9 Listing for the sequential dense LU-decomposition 529
25.10 Listing for the sequential dense LU-decomposition with pivoting 530
25.11 Listing for sequential dense LU-substitution with pivoting 531
25.12 Listing for solving a linear system of equations using the Thomas algorithm 533
26.1 Listing for matrix/vector multiplication 543
26.2 Listing for matrix evaluation 543
26.3 Listing for vector evaluation 544
26.4 Listing for Newton’s method for solving nonlinear systems of equations 545
26.5 Listing for applying the Newton’s method solver 546
27.1 Listing for Euler’s method for solving ODEs 553
27.2 Listing for the backward Euler method for solving ODEs 557
27.3 Listing for the Crank-Nicolson method for solving ODEs 561
27.4 Listing for the Adams-Bashforth method for solving ODEs 567
27.5 Listing for the Adams-Moulton method for solving ODEs 571
27.6 Listing for the fourth order Runge-Kutta method for solving ODEs 574
27.7 Listing for the Euler method applied to solving higher-order ODEs and systems of ODEs 582
27.8 Listing for the fourth-order Runge-Kutta method applied to solving higher-order ODEs and systems of ODEs 584
27.9 Listing for application examples of the fourth-order Runge-Kutta method applied to solving higher-order ODEs and systems of ODEs 587
27.10 Listing for application examples of the fourth-order Runge-Kutta method applied to solving the pendant drop ODE 589
28.1 Listing for solving a Poisson equation numerically (part 1) 598
28.2 Listing for solving a Poisson equation numerically (part 2) 599
28.3 Listing for solving a Poisson equation numerically (part 3) 600
28.4 Listing for solving a Poisson equation numerically using SOR in C 602
28.5 Listing for solving a Poisson equation numerically (part 4) 604
28.6 Listing for solving a Poisson equation numerically (part 5) 606
29.1 Listing for the Galerkin method (part 1) 614
29.2 Listing for the adapted Galerkin method (part 2) 616
32.1 Listing for solving a linear system of equations using the Thomas algorithm 666
32.2 Mesh definition for two-dimensional FEM 673
32.3 Helper functions for two-dimensional FEM 674
32.4 Function Initialize required for two-dimensional FEM 674
32.5 Single triangle contribution for two-dimensional FEM 676
32.6 Mesh processing for two-dimensional FEM 676
32.7 Solving the mesh in two-dimensional FEM 677
32.8 Applying two-dimensional FEM using the implemented functions 677
33.1 Listing for preparing a rectangular grid 682
33.2 Listing for preparing a circular grid 683
33.3 Listing for solving time-dependent flow problems 683
33.4 Listing for solving transient flow problems numerically (part 1) 685
33.5 Listing for solving transient flow problems numerically (part 2) 687
33.6 Listing for solving a space-transient flow problem while neglecting convection 690
33.7 Listing for solving transient flow problems numerically (part 3) 690
33.8 Listing for solving a space-transient flow problem taking convection into account 691
33.9 Listing for solving transient flow problems numerically (part 4) 692
33.10 Listing for solving transient flow problems numerically (part 5) 698
34.1 Helper structures used for the implementation of the three-dimensional solver 718
34.2 Body of the three-dimensional solver implementation 720
34.3 The macro ABS of the three-dimensional solver implementation 720
34.4 Block 1 of the three-dimensional solver implementation 722
34.5 Block 2 of the three-dimensional solver implementation 722
34.6 Macro UpdateFlowVariableCorrectIndex of the three-dimensional solver implementation 723
34.7 Macros UpdateFlowVariableValuesAll and UpdateFlowVariableValuesSingle of the three-dimensional solver implementation 723
34.8 Macros UpdateFlowVariableValuesDifferenceAll and UpdateFlowVariableValuesDifference of the three-dimensional solver implementation 725
34.9 Block 3 of the three-dimensional solver implementation 726
34.10 Block 4 of the three-dimensional solver implementation 726
34.11 The macros UpdateFlowVariableDoNeumann and UpdateFlowVariableDoNeumannSingle of the three-dimensional solver implementation 726
34.12 Maple worksheet for solving the flow cases using the three-dimensional solver 727
34.13 Maple worksheet for solving case 1 using the three-dimensional solver 729
34.14 Maple worksheet for solving case 2 using the three-dimensional solver 731
34.15 Maple worksheet for solving case 3 using the three-dimensional solver 733
34.16 Maple worksheet for solving case 4 using the three-dimensional solver 735
34.17 Maple worksheet for solving case 5 using the three-dimensional solver 737
34.18 Maple worksheet for solving case 6 using the three-dimensional solver 740