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