## Finite Difference Computing with Exponential Decay ModelsThis text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular. |

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Finite Difference Computing with Exponential Decay Models Hans Petter Langtangen No preview available - 2016 |

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Â-rule algorithm amplification factor applied array Backward Euler scheme command command-line command-line arguments constant convergence rates corresponding Crank–Nicolson scheme Creative Commons license curve DEBUG decay decay.py derivative difference equation dimensionless doc string doctest dt_values exact solution example exponential Exponential Decay expression Filename finite difference finite difference methods format formula Forward Euler scheme implementation initial condition integer interface interval Leapfrog scheme linear mathematical Matplotlib matplotlib.pyplot mesh points Meshfree Methods module file Newton’s nonlinear norm np.linspace(0 Nt+1 numerical methods numerical solution numpy output parameters parser Partial Differential Equations plot polynomial pytest Python Python function radioactive decay real numbers rounding errors Runge–Kutta method scaled Sect simulation solve solver function solver(I step sympy sys.argv Taylor polynomial temperature Terminal Terminal test function theta unC1 unit testing values variable verification write