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送料無料 日付更新(2017年7月)

1,000円以上の注文で3%OFFクーポン(0922-28)

目次

  • Chapter 1 Introduction
    • 1.1 Computer as telescope
    • 1.2 Four processes for numerical simulation on screen
    • 1.3 Formulation/Modeling
    • 1.4 Transformation/Discrete approximation
    • 1.5 Computation/Algorithm
    • 1.6 Computation/Coding
    • 1.7 Visualization
    • 1.8 Feedbacks/Validation+Verification
    • 1.9 Remarks
  • Chapter 2 Partial Differential Equations and Analytical Solutions−Hyperbolic,Parabolic and Elliptic equations−
    • 2.1 Type of partial differential equation
    • 2.2 Type of boundary condition
    • 2.3 Preliminary for analytical solution
    • 2.4 Hyperbolic PDE−Analytical solution of wave equation−
    • 2.5 Parabolic PDE−Analytical solution of wave equation−
    • 2.6 Elliptic PDE−Analytical solution of Poisson equation
  • Chapter 3 Finite Difference Equation and Typical Scheme−Discrete approximation and scheme−
    • 3.1 Mesh system on screen
    • 3.2 Difference quotient for differential operator
    • 3.3 Discrete approximation for wave equation
    • 3.4 Discrete approximation for advection equation
    • 3.5 Discrete approximation for heat conduction equation
    • 3.6 Discrete approximation for the Poisson equation
    • 3.7 Nature of finite difference method comparing with FEM
  • Chapter 4 Change in qualitative property of system−Initial value problem−
    • 4.1 Preliminary for finite difference scheme
    • 4.2 Stability of dynamic system on screen
    • 4.3 Advection diffusion equation
    • 4.4 von Neumann stability analysis
    • 4.5 In connection of consistency with numerical instability on screen
    • 4.6 Artificial viscosity
    • 4.7 Ill‐posed problem
  • Chapter 5 Iterative Method for Elliptic Equation−Boundary value problem−
    • 5.1 Model question Q7
    • 5.2 Model question Q8,Q9 and Q10
    • 5.3 Basic concept of iterative methods
    • 5.4 Jacobi method
    • 5.5 Gauss−Seidel method
    • 5.6 SOR method−Successive Over Relaxation method−
    • 5.7 Analogy of iteration to solving time‐dependent question
    • 5.8 Conjugate Gradient method
    • 5.9 Basic aspects of direct method
  • Chapter 6 Applications−Mixed natures of PDEs−
    • 6.1 Laplace equation with variable coefficient on screen−Inner and outer iteration for nonlinear system−
    • 6.2 Poisson equation with variable coefficient−Inner and outer iteration for nonlinear equation−
    • 6.3 Soliton−Boussinesq Equation,solitary waves or balls−
    • 6.4 Burgers Equation−Numerical treatment of discontinuity−
    • 6.5 Back step flow−Basic algorithm for mixed nature of PDEs−
    • 6.6 Collision of droplets−VOF:Algorithm for flow with free surface−
    • 6.7 Blow down−Semi‐implicit scheme for flow with phase change and wave propagation−