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Numerical Software 1, academic year 2024/25

Week 1, September 30, 2024

  • Introduction of the aims and scopes of the lecture, presentation pres-intro24.pdf
  • Introduction to scientific computing, lecture notes NumSoft.pdf , Chapter 1
  • Types of numerical software, lecture notes NumSoft.pdf , Chapter 2

    Week 2, October 7, 2024

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

  • Tutorial : instalation of Linux and software packages (gfortran, gnuplot, text editor) tutorial1_linux.pdf
  • Linux, basic commands, lecture notes NumSoft.pdf , Chapters 4
  • direct link for instalation

    Week 3, October 14, 2024

  • Machine arithmetic, lecture notes NumSoft.pdf , Chapter 3
  • Fortran: basic introduction, lecture notes NumSoft.pdf , Chapters 5

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

    Week 4, October 21, 2024

  • Efficient programming, lecture notes NumSoft.pdf , Section 6.1
  • The use of the cache memory, lecture notes NumSoft.pdf , Section 6.2.

  • Tutorial : use of the cache memory tutorial3_cache.pdf , codes for tutorial

    Week 5, October 28, 2024

  • Holidays, no lecture

    Week 6, November 4, 2024

  • Fundamentals of adaptations, lecture notes NumSoft.pdf , Chapters 8
  • Tutorial : LAPACK and BLAS libraries tutorial4_lapack.pdf see also lecture notes NumSoft.pdf , Chapters 7, codes for tutorial

    Week 7, November 11, 2024

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

  • Tutorial : Newton-Cottes formulas, orders of accuracy and error estimates tutorial5_quadrature.pdf , codes for tutorial (NC_test.tgz)

    Week 8, November 18, 2024

  • Numerical quadratures, Error estimates and adaptivity, lecture notes NumSoft.pdf , Chapters 9
  • codes QUANC8, Q1DA, lecture notes NumSoft.pdf Chapters 9
  • integ_adaptation.pdf – animation of the local and global adaptation

  • Tutorial : Main task # 1, tutorial6_quanc8_q1da.pdf (Codes QUANC8 and Q1DA are here )

    Week 9, November 25, 2024

  • quiz1.pdf
  • Numerical quadratures, several comments to the Main task # 1, lecture notes NumSoft.pdf , Chapters 9
  • Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • problem formulation, stability, stiff problems

  • Tutorial : Main task # 1, tutorial6_quanc8_q1da.pdf (Codes QUANC8 and Q1DA are here )

    Week 10, December 2, 2024

  • 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
  • adapt_ODE.pdf principle of the adaptive choice of the time step

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

    Week 11, December 9, 2024

  • quiz2.pdf
  • Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • explicit Euler method for stiff systems
  • implicit Euler method, stability, accuracy
  • implicit Euler method for stiff systems
  • quiz3.pdf
  • Runge-Kutta methods

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

    Week 12, December 16, 2024

  • Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • Runge-Kutta methods
  • estimates of the local error
  • adaptive setting of the time step
  • quiz4.pdf
  • quiz5.pdf
  • some comments related to the Main task 2

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

    Week 13, January 6, 2025

  • Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
  • multistep implicit method, predictor-corrector method
  • solution of nonlinear systems using Newton method
  • code SODE, practical issues
  • implicit Runge-Kutta method, DIRK (diagonally implicit RK)
  • IM-EX methods (implicit-explicit methods)

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