Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

3.5 Numerical integration 59
with
( 0 )= 0 (3.143)
Result by substituting ·
( 0 )= ( 0 ):
( 0 + ) = ( 0 )+( 0 )+O ¡ 2¢ (3.144)
Recursion formula (see Fig. 3.1):
+1 = + (3.145)
+1 = + ( ) (3.146)
Problem: Large errors for practical step sizes.
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Figure 3.1: Euler method.
3.5.3 Runge-Kutta methods
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2 order Runge-Kutta method:
Initial value problem:
with
·
= ( ) (3.147)
( 0 )= 0 (3.148)