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【ネットストア】カレンダー全品ポイント最大10倍キャンペーン

カレンダーポイント最大10倍キャンペーン(~12/31)

目次

  • Chapter1 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
  • Chapter2 Partial Differential Equation and Analytical Solution−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 heat conduction equation−
    • 2.6 Elliptic PDE−Analytical solution of Poisson equation−
  • Chapter3 Finite Difference Equation and Computational Molecules−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
  • Chapter4 Change in Qualitative Nature 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 Connection between consistency and numerical instability on screen
    • 4.6 Artificial viscosity
    • 4.7 Ill‐posed problem
  • Chapter5 Iterative method for Elliptic Difference Equation−Boundary Value Problem−
    • 5.1 Model question Q7
    • 5.2 Model question Q8,Q9 and Q10
    • 5.3 Basic aspect 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
  • Chapter6 Applications−Mixed Natures of PDEs−
    • 6.1 Laplace equation with variable coefficient−Inner and outer iteration for nonlinear system−
    • 6.2 Poisson equation with variable coefficient−Inner and outer iteration for nonlinear system−
    • 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 water droplets−VOF:Algorithm for flow with free surface−
    • 6.7 Blow down−Semi‐implicit scheme for flow with phase change and wave propagation−

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