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Numerical Software 1, academic year 2021/22

Week 1, October 4, 2021

  • Introduction of the aims and scopes of the lecture, presentation pres-intro21.pdf

  • Introduction to scientific computing, lecture notes NumSoft.pdf , Chapter 1

  • Types of numerical software, lecture notes NumSoft.pdf , Chapter 2

    Week 2, October 11, 2021

  • Machine arithmetic, lecture notes NumSoft.pdf , Chapter 3

  • Tutorial : instalation of Linux and software packages (gfortran, gnuplot, text editor) tutorial1_linux.pdf

    Week 3, October 18, 2021

  • Machine arithmetic, lecture notes NumSoft.pdf , Chapter 3

  • Fortran, lecture notes NumSoft.pdf , Chapters 5

  • Tutorial : simple codes in gfortran, examples of machine arithmetic tutorial2_gfort+FF.pdf

    Week 4, October 25, 2021

  • Lecture: Fortran, efficient programming, cache memory, lecture notes NumSoft.pdf , Chapters 5-6

  • Tutorial : simple codes in gfortran, use of the cache memory tutorial3_cache.pdf
  • for tutorial, download all codes from the link Efficient programming (use of the cache memory) (a separate directory is recommended)

    Week 5, November 1, 2021

  • Lecture: Fundamentals of adaptations, lecture notes NumSoft.pdf , Chapters 8

  • Lecture: Numerical quadratures – introduction, lecture notes NumSoft.pdf , Chapters 9

  • Tutorial : LAPACK and BLAS libraries tutorial4_lapack.pdf see also lecture notes NumSoft.pdf , Chapters 7

    Week 6, November 8, 2021

  • Lecture: Numerical quadratures, lecture notes NumSoft.pdf , Chapters 9

  • Tutorial : Newton-Cottes formulas, orders of accuracy and error estimates tutorial5_quadrature.pdf
  • supporting source file NC_test.tgz here

    Week 7, November 15, 2021

  • quiz1.pdf
  • Lecture: introduction to the codes QUANC8, Q1DA, lecture notes NumSoft.pdf Chapters 9
  • integ_adaptation.pdf – animation of the local and global adaptation

  • Tutorial : Main task # 1, Tutorial 6 (Codes QUANC8 and Q1DA)

    Week 8, November 22, 2021

  • Lecture: Numerical quadratures, several comments to the Main task # 1, lecture notes NumSoft.pdf , Chapters 9
  • Solution of ordinary differential equations, stability, stiff systems lecture notes NumSoft.pdf , Chapters 10

  • Tutorial : Main task # 1, Tutorial 6 (Codes QUANC8 and Q1DA)

    Week 9, November 29, 2021

  • Lecture: Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • local, global errors, stability of the Euler method
  • estimate of the local errors

  • Tutorial : Solution of ODE by the Euler method, adaptive choice of the time step Tutorial 7 (ODE, simple test cases), page 1.

    Week 10, December 6, 2021

  • adapt_ODE.pdf principle of the adaptive choice of the time step
  • quiz2.pdf
  • Lecture: Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • stiff systems solved by the explicit Euler method
  • implicit Euler method, stability, accuracy

  • Tutorial : Solution of stiff ODE by the explicit and implcit Euler methods Tutorial 7 (ODE, simple test cases), page 2.

    Week 11, December 13, 2021

  • Lecture: Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • Runge-Kutta methods
  • multi-step methods
  • estimates of the local error
  • adaptive setting of the time step

  • Tutorial : Main task 2, codes RKF45, DOPRI5, solution of the given ODEs Tutorial 8

    Week 12, December 20, 2021

  • Lecture: Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • quiz4.pdf
  • quiz5.pdf
  • some comments related to the Main task 2
  • solution of large systems of ODEs

  • Tutorial : Main task 2, codes RKF45, DOPRI5, solution of the given ODEs Tutorial 8

    Week 13, January 3, 2022

  • Lecture: Time discontinuous Galerkin method,
  • Tutorial : Main task 2, codes RKF45, DOPRI5, solution of the given ODEs Tutorial 8