Introduction to Scientific Computing - Tutorial 13: Recapitulation

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Homogeneous — roots Difference Complex ρ = α ± βi Differential Complex ρ = α ± βi µ := √ α 2 + β 2 tan φ = β/α x n = µ n (Acos(nφ) + iBsin(nφ)) x = e αt (Acos(βt) + iBsin(βt)) 1. Februar 2013 Bojana Rosic Introduction to Scientific Computing Seite 6
Non-homogeneous- Particular solution Difference Differential x n = x nh + x np x = x h + x p x h = Ce pt , x p = c(t)e pt variation of constant 1. Februar 2013 Bojana Rosic Introduction to Scientific Computing Seite 7
Page 1 and 2: Introduction to Scientific Computin
Page 3 and 4: Difference vs. Differential equatio
Page 5: Homogeneous — roots Difference Di
Page 9 and 10: Stability If there is just one root
Page 11 and 12: Consistency Write numerical method
Page 13 and 14: Numerical Integration of ODEs ẋ =
Page 15 and 16: Stability of linear multistep metho
Page 17 and 18: Runge-Kutta methods The general for
Page 19 and 20: Fixed-point iterations We want to s
Page 21 and 22: Newton method F(x) = 0 F(x) = F(x 0
Page 23 and 24: Previous HW- Runge-Kutta-Fehlberg m
Page 29 and 30: we may find ˆb 2 and ˆb 3 as well
Page 31 and 32: Previous HW- Skydiver mechanics I w
Page 33 and 34: Previous HW- Skydiver mechanics II
Page 35 and 36: Previous HW- Skydiver mechanics II
Page 37 and 38: Previous HW- Skydiver mechanics ∫
Page 39 and 40: MATLAB % main script clear variable
Page 41 and 42: MATLAB if t

Introduction to Scientific Computing - Tutorial 13: Recapitulation

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