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Numerical Software 1, academic year 2023/24
Week 1, October 3, 2023
Introduction of the aims and scopes of the lecture,
presentation pres-intro23.pdf
Introduction to scientific computing, lecture notes NumSoft.pdf , Chapter 1
Types of numerical software, lecture notes NumSoft.pdf , Chapter 2
Week 2, October 10, 2023
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 17, 2023
Machine arithmetic, lecture notes NumSoft.pdf ,
Chapter 3
Linux, basic commands, lecture notes NumSoft.pdf , Chapters 4
Fortran, lecture notes NumSoft.pdf , Chapters 5
Efficient programming, lecture notes NumSoft.pdf ,
Section 6.1
Tutorial : simple codes in gfortran, examples of machine arithmetic
tutorial2_gfort+FF.pdf ,
codes for tutorial
Week 4, October 24, 2023
Efficient programming, lecture notes NumSoft.pdf ,
Section 6.1
The use of the cache memory,
lecture notes NumSoft.pdf , Section 6.2.
Fundamentals of adaptations,
lecture notes NumSoft.pdf , Chapter 8
Tutorial : use of the cache memory
tutorial3_cache.pdf ,
codes for tutorial
Week 5, October 31, 2023
Fundamentals of adaptations, lecture notes NumSoft.pdf ,
Chapters 8
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,
codes for tutorial
Week 6, November 7, 2023
Numerical quadratures, lecture notes NumSoft.pdf ,
Chapters 9
introduction to the codes QUANC8, Q1DA, 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 7, November 14, 2023
codes QUANC8, Q1DA, lecture notes NumSoft.pdf Chapters 9
integ_adaptation.pdf – animation of the local and global adaptation
quiz1.pdf
Tutorial : Main task # 1, tutorial6_quanc8_q1da.pdf
(Codes QUANC8 and Q1DA are here )
Week 8, November 21, 2023
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 9, November 28, 2023
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
quiz2.pdf
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 10, December 5, 2023
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
Tutorial : Solution of stiff ODE by the explicit and implcit Euler methods
Tutorial 7 (ODE, simple test cases),
page 2; codes are here
Week 11, December 12, 2023
Numerical solution of ordinary differential equations, lecture notes NumSoft.pdf , Chapters 10
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 12, December 19, 2023
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
Week 13, January 9, 2024
Time discontinuous Galerkin method,
space-time discretization
Tutorial : Main task 2, codes RKF45, DOPRI5, solution of the given ODEs
Tutorial 8 ,
Exams possible