Calculating the error in the solution of a system of ODEs

I have solved system of ODEs by using NDSolve. I want to calculate the error of the solutions. So far I have calculated error by plotting results of each equation.

  1. Is what I'm doing the correct way to obtain the error for my problem?
  2. I am not sure the results I am getting are accurate enough. If not, then kindly suggest some other way to calculate the error.

My code for solving the system of ODEs

s =    NDSolve[     {x''[t] == -(1/2)*y[t]*x'[t], y''[t] == x'[t],       x'[0] == -1 + x[0], y[0] == 0, x[10] == 0, y'[10] == 0},      {x, y}, {t, 20}] 

I am examining the error for the 1st equation with

Plot[(x''[t] + (1/2)*y[t]*x'[t]) /. s, {t, 1, 10}, WorkingPrecision -> 50] 

Calculating the error in the solution of a system of ODEs

and for the 2nd equation

Plot[(y''[t] + x'[t]) /. s, {t, 1, 10}, WorkingPrecision -> 50] 

Calculating the error in the solution of a system of ODEs

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Category: differential equations Time: 2016-07-30 Views: 0

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