Page - XXIII - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

ListofExercises xxiii Exercise8.12:Use a BackwardEulerSchemeforPopulationGrowth . . . . . . . 276 Exercise8.13:Use a Crank-NicolsonSchemeforPopulationGrowth . . . . . . . 277 Exercise8.14:UnderstandFiniteDifferencesviaTaylorSeries . . . . . . . . . . . . 277 Exercise8.15:TheLeapfrogMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Exercise8.16:TheRunge-KuttaThirdOrderMethod . . . . . . . . . . . . . . . . . . . . 280 Exercise8.17:TheTwo-StepAdams-BashforthMethod . . . . . . . . . . . . . . . . . . 280 Exercise8.18:TheThree-StepAdams-BashforthMethod . . . . . . . . . . . . . . . . . 282 Exercise8.19:Use a BackwardEulerSchemeforOscillations . . . . . . . . . . . . . 282 Exercise8.20:Use Heun’sMethodfor the SIRModel . . . . . . . . . . . . . . . . . . . . 283 Exercise8.21:Use Odespy to Solvea SimpleODE . . . . . . . . . . . . . . . . . . . . . . 283 Exercise8.22:Set upaBackwardEulerSchemeforOscillations . . . . . . . . . . . 284 Exercise 8.23: Set up a Forward Euler Scheme for Nonlinear and Damped Oscillations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Exercise8.24:Solvinga NonlinearODEwithBackwardEuler . . . . . . . . . . . . 285 Exercise8.25:Discretizean InitialCondition . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Exercise9.1:SimulateaDiffusionEquationbyHand . . . . . . . . . . . . . . . . . . . . 303 Exercise9.2:ComputeTemperatureVariations in theGround.. . . . . . . . . . . . . 303 Exercise9.3:Compare ImplicitMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Exercise9.4:ExploreAdaptiveand ImplicitMethods . . . . . . . . . . . . . . . . . . . . 305 Exercise9.5: Investigate theθ Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Exercise9.6:Compute theDiffusionofaGaussianPeak . . . . . . . . . . . . . . . . . . 306 Exercise9.7:VectorizeaFunctionforComputing the AreaofaPolygon . . . . 307 Exercise9.8:ExploreSymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Exercise9.9:ComputeSolutionsas t→∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Exercise9.10:SolveaTwo-PointBoundaryValueProblem . . . . . . . . . . . . . . . 309