Example 12.  Solve the I.V.P.  [Graphics:Images/Euler'sMethodMod_gr_250.gif].     Compute the Modified Euler solution to the I.V.P.

Solution 12.

[Graphics:../Images/Euler'sMethodMod_gr_251.gif]

[Graphics:../Images/Euler'sMethodMod_gr_252.gif]

[Graphics:../Images/Euler'sMethodMod_gr_253.gif]
[Graphics:../Images/Euler'sMethodMod_gr_254.gif]
[Graphics:../Images/Euler'sMethodMod_gr_255.gif]
[Graphics:../Images/Euler'sMethodMod_gr_256.gif]
[Graphics:../Images/Euler'sMethodMod_gr_257.gif]


[Graphics:../Images/Euler'sMethodMod_gr_258.gif]

[Graphics:../Images/Euler'sMethodMod_gr_259.gif]

[Graphics:../Images/Euler'sMethodMod_gr_260.gif]
[Graphics:../Images/Euler'sMethodMod_gr_261.gif]
[Graphics:../Images/Euler'sMethodMod_gr_262.gif]
[Graphics:../Images/Euler'sMethodMod_gr_263.gif]
[Graphics:../Images/Euler'sMethodMod_gr_264.gif]


[Graphics:../Images/Euler'sMethodMod_gr_265.gif]

[Graphics:../Images/Euler'sMethodMod_gr_266.gif]

[Graphics:../Images/Euler'sMethodMod_gr_267.gif]
[Graphics:../Images/Euler'sMethodMod_gr_268.gif]
[Graphics:../Images/Euler'sMethodMod_gr_269.gif]
[Graphics:../Images/Euler'sMethodMod_gr_270.gif]
[Graphics:../Images/Euler'sMethodMod_gr_271.gif]

Animation 1.  ( Modified Euler's Method  Modified Euler's Method ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004