y′=f(t,y) with Euler's MethodI'm trying to compute the approximation solution for y ′ = − 2 y + 2 − e − 4 t : 0 ≤ t ≤ 5 , y ( 0 ) = 1but the answer that I get for n = 100 intervals is −5.069 which isn't right. What's the issue with my algorithm? valueA = 0; valueB = 5; double y0 = 1; double y1 = 0; double t = 0; valueN = 100; double valueM = 0; double functionOne = 0; double h = (valueB-valueA)/valueN; for (double i = 0; i &lt;= 5.00; i+=h){ valueM = ((-2*y0) + 2 - Math.exp(-4*t)); y1 = y0 + (t * valueM); y0 = y1; t += h; } return y1;First Ten Values:1. 1.02. 0.9590634623461013. 0.90021876527331684. 0.84783139027721785. 0.81883304134288646. 0.81744666037858267. 0.83662040057777248. 0.86467718279376959. 0.892176829360891710. 0.914833183236375211. 0.9323323583816936

Question

y′=f(t,y) with Euler&#039;s MethodI&#039;m trying to compute the approximation solution for      y    ′    =  −  2  y  +  2  −      e          −      4      t        :  0  ≤  t  ≤  5  ,  y  (  0  )  =  1but the answer that I get for   n  =  100 intervals is −5.069 which isn&#039;t right. What&#039;s the issue with my algorithm?    valueA = 0;    valueB = 5;    double y0 = 1;    double y1 = 0;    double t = 0;    valueN = 100;    double valueM = 0;    double functionOne = 0;    double h = (valueB-valueA)/valueN;    for (double i = 0; i &amp;lt;= 5.00; i+=h){    valueM = ((-2*y0) + 2 - Math.exp(-4*t));    y1 = y0 + (t * valueM);    y0 = y1;    t += h;    }    return y1;First Ten Values:1. 1.02. 0.9590634623461013. 0.90021876527331684. 0.84783139027721785. 0.81883304134288646. 0.81744666037858267. 0.83662040057777248. 0.86467718279376959. 0.892176829360891710. 0.914833183236375211. 0.9323323583816936

Katelynn Petersen · Accepted Answer

With       t          n      +      1        =      t    n    +  δ  t your algorithm is essentially   y  (      t          n      +      1        )  =  y  (      t    n    )  +  δ  t      y    ′    (      t    n    ).I think the incriminated line is  y1 = y0 + (t * valueM);which should be  y1 = y0 + (h * valueM);

Baylee Atkinson · Accepted Answer

Tthanks a lot

I'm trying to compute the approximation solution for y′=−2y+2−e^(−4t):0<=t<=5,y(0)=1 but the answer that I get for n=100 intervals is −5.069 which isn't right. What's the issue with my algorithm?

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