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  • Hutchinson, I. H. (Ian H.), 1951-
     
     Subjects
     
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  • Numerical analysis.
     
  •  
  • Mensuration.
     
  •  
  • Number concept.
     
  •  
  • Matrices.
     
  •  
  • Mathematics -- Study and teaching.
     
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  •  Hutchinson, I. H. (Ian H.), 1951-
     
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  •  A student's guide to...
     
     
     
     MARC Display
    A student's guide to numerical methods / Ian H. Hutchinson, Massachusetts Institute of Technology.
    by Hutchinson, I. H. (Ian H.), 1951-
    View full image
    Subjects
  • Numerical analysis.
  •  
  • Mensuration.
  •  
  • Number concept.
  •  
  • Matrices.
  •  
  • Mathematics -- Study and teaching.
  • ISBN: 
    9781107095670
    1107095670
    9781107479500
    1107479509
    Description: 
    xiv, 207 pages : illustrations ; 24 cm
    Contents: 
    pt. I. Fitting functions to data. Exact fitting ; Approximate fitting ; Tomographic image reconstruction ; Efficiency and non-linearity -- pt. II. Ordinary differential equations. Reduction to first order ; Numerical integration of initial-value problems ; Multidimensional stiff equations : implicit schemes ; Leap-frog schemes -- pt. III. Two-point boundary conditions. Examples of two-point problems ; Shooting ; Direct solution ; Conservative differences, finite volumes -- pt. IV. Partial differential equations. Examples of partial differential equations ; Classification of partial differential equations ; Finite-difference partial derivatives -- pt. V. Diffusion. parabolic partial differential equations. Diffusion equations ; Time-advance choices and stability ; Implicit advancing matrix method ; Multiple space dimensions ; Estimating computational cost -- pt. VI. Elliptic problems and iterative matrix solution. Elliptic equations and matrix inversion ; Convergence rate ; Successive over-relaxation ; Iteration and non-linear equations -- pt. VII. Fluid dynamics and hyperbolic equations. The fluid momentum equation ; Hyperbolic equations ; Finite differences and stability -- pt. VIII. Boltzmann's equation and its solution. The distribution function ; Conservation of particles in phase-space ; Solving the hyperbolic Boltzmann equation ; Collision term -- pt. IX. Energy-resolved diffusive transport. Collisions of neutrons ; Reduction to multigroup diffusion equations ; Numerical representation of multigroup equations -- pt. X. Atomistic and particle-in-cell simulation. Atomistic simulation ; Particle-in-cell codes -- pt. XI. Monte Carlo techniques. Probability and statistics ; Computational random selection ; Flux integration and injection choice -- pt. XII. Monte Carlo radiation transport. Transport and collisions ; Tracking, tallying, and statistical uncertainty -- pt. XIII. Next steps. Finite-element methods ; Discrete Fourier analysis and spectral methods ; Sparse-matrix iterative Krylov solution ; Fluid evolution schemes -- Appendix A. Summary of matrix algebra. Vector and matrix multiplication ; Determinants ; Inverses ; Eigenanalysis.
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