Mathematics & Science Learning Center
Computer Laboratory

Numerical Methods for Solving Differential Equations

Euler's Method

Using the Method with Mathematica

(continued from last page...)

Your commands should have resulted in:

prelimsol2=euler[x+2y, {x,0,1}, {y,0}, 20]

{{0, 0}, {0.05, 0}, {0.1, 0.0025}, {0.15, 0.00775},
   {0.2, 0.016025}, {0.25, 0.0276275}, {0.3, 0.0428903},
   {0.35, 0.0621793}, {0.4, 0.0858972}, {0.45, 0.114487},
   {0.5, 0.148436}, {0.55, 0.188279}, {0.6, 0.234607}, 
   {0.65, 0.288068}, {0.7, 0.349375}, {0.75, 0.419312},
   {0.8, 0.498743}, {0.85, 0.588618}, {0.9, 0.689979},
   {0.95, 0.803977}, {1., 0.931875}}

MatrixForm[prelimsol2]

The last point is now (1.00, 0.931875), which is still not as accurate as we'd like. (Remember, it's supposed to be (1.00, 1.097264).) It seems obvious that the increased number of points is responsible for the increased accuracy! To get even greater accuracy, therefore, instruct Mathematica to recalculate the solution a third time, now using 100 steps.

Let's go look at your results...

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