Matlab Database > Ordinary Differential Equations > Implicit vs. Explicit Euler

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Title: Implicit vs. Explicit Euler
Author: Andreas Klimke
E-Mail: andreasklimke-AT-gmx.de
Institution: Technische Universität München
Description: Compares implicit and explicit Euler's method for variable number of steps n.
The equation solved is the spring-mass-system with the following parameters:
ODE: m*x''(t) = F(t)-c*x(t)
              
               {  20*t              t <  5
   with F(t) = {  20*(10-t)    5 <= t <= 10
               {  0                 t >  10

           c = 4.5 * 10^9 / 150^3
           m = 5 * 10^3
 
        x(0) = 0
       x'(0) = 0
One can see the numerical damping effect of the implicit method compared to the numerical instability of the explicit method (solution -> infinity for t -> infinity).
Keywords: ODE, spring-mass-system, Euler, implicit, explicit
File Name: ems_imp_exp.m
File Size: 2 KB
File Version: 1.0
Matlab Version: 6.1
Date: 2002-07-05
Downloads: 9836
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